diff --git a/crates/engine/src/cancel_tests.rs b/crates/engine/src/cancel_tests.rs
new file mode 100644
index 0000000..d9320dd
--- /dev/null
+++ b/crates/engine/src/cancel_tests.rs
@@ -0,0 +1,130 @@
+//! A cancelled job ([`fieldcraft_model::progress::Progress::cancel`]) stops every solver and
+//! mesher promptly with `cancelled` and leaves the model as it was.
+
+use std::time::{Duration, Instant};
+
+use fieldcraft_geometry::sample::Plate;
+use fieldcraft_model::progress::{self, Progress};
+use serde_json::{Value, json};
+
+use crate::Session;
+use crate::sample::impact;
+
+/// How long a cancelled command may keep running: one increment, time step or pass, far
+/// below the minutes the runs below would take uncancelled.
+const PROMPT: Duration = Duration::from_secs(5);
+
+/// Run `command` on `s` the way a job does and cancel it once it reports the stage `stage`
+/// (mid-run), or before it starts (`None`): it must fail with `cancelled`, soon after, leaving
+/// the model and the journal as they were.
+fn cancel(s: &mut Session, command: &str, params: Value, stage: Option<&str>) {
+    let (model, journal) = (s.model.clone(), s.journal.len());
+    let p = Progress::new();
+    if stage.is_none() {
+        p.cancel();
+    }
+    let (r, waited) = std::thread::scope(|scope| {
+        let worker = {
+            let p = p.clone();
+            let s = &mut *s;
+            let params = params.clone();
+            scope.spawn(move || progress::scoped(Some(p), || s.execute(command, &params)))
+        };
+        let mut at = Instant::now();
+        if let Some(stage) = stage {
+            let deadline = Instant::now() + Duration::from_secs(600);
+            while !worker.is_finished() && Instant::now() < deadline {
+                let now = p.snapshot();
+                if now.stage.starts_with(stage) && now.done > 0.0 {
+                    at = Instant::now();
+                    p.cancel();
+                    break;
+                }
+                std::thread::sleep(Duration::from_millis(1));
+            }
+            assert!(p.is_cancelled(), "{command}: never reached stage `{stage}` ({:?})", p.snapshot());
+        }
+        let r = worker.join().unwrap();
+        (r, at.elapsed())
+    });
+    let e = r.expect_err(&format!("{command}: ran to the end although cancelled"));
+    assert!(e.is_cancelled(), "{command}: {e}");
+    assert_eq!(e.to_string(), "cancelled", "{command}");
+    assert!(waited < PROMPT, "{command}: stopped {waited:?} after the cancel");
+    assert!(s.model == model, "{command}: the model changed");
+    assert_eq!(s.journal.len(), journal, "{command}: journalled");
+}
+
+/// A sample's script run on a fresh session.
+fn session(script: &Value) -> Session {
+    let mut s = Session::default();
+    s.run_script(script).unwrap();
+    s
+}
+
+fn plate() -> (crate::tests::TempDir, Session) {
+    let (dir, path) = crate::tests::sample_design_file(&Plate::default());
+    let mut s = Session::default();
+    s.execute("geometry.open", &json!({"path": path})).unwrap();
+    (dir, s)
+}
+
+#[test]
+fn explicit_stops_between_time_steps() {
+    // A hundred times as long as the sample: hundreds of thousands of increments.
+    let mut script = impact();
+    for c in script.as_array_mut().unwrap() {
+        if c["command"] == "model.step.create" {
+            let p = &mut c["params"]["procedure"];
+            (p["end_time"], p["output_interval"], p["history_interval"]) = (json!(4e-3), json!(4e-4), json!(2e-5));
+        }
+    }
+    let mut s = session(&script);
+    cancel(&mut s, "solve.explicit", json!({}), Some("Time"));
+}
+
+#[test]
+fn fluid_stops_between_lattice_steps() {
+    let mut s = Session::default();
+    s.execute("file.sample", &json!({"name": "flow-past"})).unwrap();
+    cancel(&mut s, "solve.fluid", json!({}), Some("Fluid steps"));
+}
+
+#[test]
+fn nonlinear_stops_between_increments() {
+    let mut s = Session::default();
+    s.execute("file.sample", &json!({"name": "rubber-seal"})).unwrap();
+    cancel(&mut s, "solve.nonlinear", json!({}), Some("Load factor"));
+}
+
+#[test]
+fn transient_heat_stops_between_increments() {
+    let mut s = Session::default();
+    s.execute("file.sample", &json!({"name": "heated-bracket"})).unwrap();
+    s.execute(
+        "model.step.create",
+        &json!({"name": "Warm", "procedure": {"type": "heat_transfer", "transient": {"end_time": 1e5, "increment": 1}},
+            "boundary_conditions": ["Heater"], "loads": ["Air"]}),
+    )
+    .unwrap();
+    cancel(&mut s, "solve.heat", json!({"step": "Warm"}), Some("Time increment"));
+}
+
+#[test]
+fn static_frequency_and_solve_all_stop_at_the_factorization() {
+    let mut s = Session::default();
+    s.execute("file.sample", &json!({"name": "cantilever"})).unwrap();
+    cancel(&mut s, "solve.static", json!({}), None);
+    cancel(&mut s, "solve.frequency", json!({}), None);
+    cancel(&mut s, "solve.run", json!({}), None);
+}
+
+#[test]
+fn meshers_stop_and_leave_no_mesh() {
+    let (_dir, mut s) = plate();
+    cancel(&mut s, "mesh.tet.generate", json!({"body": "Body1", "size": 0.4}), Some("Refinement round"));
+    cancel(&mut s, "mesh.tet.generate", json!({"body": "Body1", "size": 2.5}), None);
+    cancel(&mut s, "mesh.hex.generate", json!({"body": "Body1", "size": 2.5}), None);
+    cancel(&mut s, "mesh.hex.octree", json!({"body": "Body1", "size": 5.0, "max_depth": 2}), None);
+    assert!(s.model.nodes().is_empty());
+}
diff --git a/crates/engine/src/cmd/hex.rs b/crates/engine/src/cmd/hex.rs
index a4da344..f508b21 100644
--- a/crates/engine/src/cmd/hex.rs
+++ b/crates/engine/src/cmd/hex.rs
@@ -220,7 +220,10 @@ pub(super) fn hex_blocks(s: &mut Session, p: &Value) -> Result<Value> {
         seeds: super::seeds::edge_seeds(s)?,
         ..HexOptions::default()
     };
-    let cm = hex_mesh_cells(&cells, &UniformSize(h), &options).map_err(|e| EngineError::Params(e.to_string()))?;
+    let cm = hex_mesh_cells(&cells, &UniformSize(h), &options).map_err(|e| match e {
+        fieldcraft_mesh::Error::Model(fieldcraft_model::Error::Cancelled) => EngineError::Model(fieldcraft_model::Error::Cancelled),
+        e => EngineError::Params(e.to_string()),
+    })?;
     let m = &cm.mesh;
     // Replace the cells' meshes (replace.rs); other bodies and the definitions stay.
     let model = &mut s.model;
@@ -349,7 +352,7 @@ pub(super) fn hex_body(p: &Value, b: &Input, method: HexMethod, quadratic: bool,
         seeds: b.seeds.clone(),
         ..HexOptions::default()
     };
-    hex_mesh(&surface, &b.surfaces, &UniformSize(h), &options).map_err(|e| EngineError::Params(format!("body `{}`: {e}", b.name)))
+    hex_mesh(&surface, &b.surfaces, &UniformSize(h), &options).map_err(|e| EngineError::of_body(&b.name, e))
 }
 
 /// Add one body's hex mesh after the model's largest labels, tagging the elements with the body
diff --git a/crates/engine/src/cmd/mesh.rs b/crates/engine/src/cmd/mesh.rs
index 0005bb9..4e9f614 100644
--- a/crates/engine/src/cmd/mesh.rs
+++ b/crates/engine/src/cmd/mesh.rs
@@ -271,7 +271,7 @@ pub(super) fn mesh_body(
             surface_volume: surface.volume(),
         })
     };
-    mesh().map_err(|e| if several { EngineError::Params(format!("body `{}`: {e}", input.name)) } else { e })
+    mesh().map_err(|e| if several && !e.is_cancelled() { EngineError::Params(format!("body `{}`: {e}", input.name)) } else { e })
 }
 
 fn tet_generate(s: &mut Session, p: &Value) -> Result<Value> {
diff --git a/crates/engine/src/cmd/octree.rs b/crates/engine/src/cmd/octree.rs
index 889a271..fbcad08 100644
--- a/crates/engine/src/cmd/octree.rs
+++ b/crates/engine/src/cmd/octree.rs
@@ -60,7 +60,7 @@ fn hex_octree(s: &mut Session, p: &Value) -> Result<Value> {
         let surface = BoundarySurface::new(&b.mesh.positions, &b.mesh.triangles, &b.mesh.tri_face, &surface_options)
             .map_err(|e| EngineError::Params(format!("body `{}`: {e}", b.name)))?;
         let left = OctreeOptions { max_elements: options.max_elements.saturating_sub(total).max(1), ..options.clone() };
-        let mesh = octree_hex_mesh(&surface, &UniformSize(h), &left).map_err(|e| EngineError::Params(format!("body `{}`: {e}", b.name)))?;
+        let mesh = octree_hex_mesh(&surface, &UniformSize(h), &left).map_err(|e| EngineError::of_body(&b.name, e))?;
         total += mesh.hexes.len();
         meshes.push((b, mesh));
     }
diff --git a/crates/engine/src/cmd/solve.rs b/crates/engine/src/cmd/solve.rs
index e7be9e7..abde3fc 100644
--- a/crates/engine/src/cmd/solve.rs
+++ b/crates/engine/src/cmd/solve.rs
@@ -201,7 +201,9 @@ fn run_all(s: &mut Session, _: &Value) -> Result<Value> {
     let count = steps.len();
     for (index, (name, procedure, solve)) in steps.into_iter().enumerate() {
         fieldcraft_model::progress::step(&name, index + 1, count);
-        let summary = solve(s, &json!({"step": name})).map_err(|e| EngineError::Params(format!("step `{name}`: {e}")))?;
+        fieldcraft_model::progress::check()?;
+        let summary =
+            solve(s, &json!({"step": name})).map_err(|e| if e.is_cancelled() { e } else { EngineError::Params(format!("step `{name}`: {e}")) })?;
         done.push(json!({"step": name, "procedure": procedure, "summary": summary}));
     }
     Ok(json!({"steps": done}))
diff --git a/crates/engine/src/lib.rs b/crates/engine/src/lib.rs
index cd903a6..8810584 100644
--- a/crates/engine/src/lib.rs
+++ b/crates/engine/src/lib.rs
@@ -79,6 +79,29 @@ pub enum EngineError {
 }
 
 impl EngineError {
+    /// Whether the command stopped because it was cancelled
+    /// ([`fieldcraft_model::progress::Progress::cancel`]).
+    pub fn is_cancelled(&self) -> bool {
+        use fieldcraft_model::Error::Cancelled;
+        matches!(
+            self,
+            EngineError::Model(Cancelled)
+                | EngineError::Mesh(fieldcraft_mesh::Error::Model(Cancelled))
+                | EngineError::Solver(fieldcraft_solver::Error::Model(Cancelled))
+                | EngineError::Explicit(fieldcraft_explicit::Error::Model(Cancelled))
+                | EngineError::Fluid(fieldcraft_lbm::Error::Model(Cancelled) | fieldcraft_lbm::Error::Mesh(fieldcraft_mesh::Error::Model(Cancelled)))
+        )
+    }
+
+    /// A body's mesher failure as a parameter problem naming the body, or the cancellation as
+    /// it is.
+    pub(crate) fn of_body(body: &str, e: fieldcraft_mesh::Error) -> Self {
+        match e {
+            fieldcraft_mesh::Error::Model(fieldcraft_model::Error::Cancelled) => EngineError::Model(fieldcraft_model::Error::Cancelled),
+            e => EngineError::Params(format!("body `{body}`: {e}")),
+        }
+    }
+
     /// A problem with the parameter at `path` (`elastic/young`).
     pub fn param(path: impl Into<String>, kind: schema::ProblemKind) -> Self {
         Self::Param(schema::Problem::at(path, kind))
@@ -440,6 +463,9 @@ impl Session {
     }
 }
 
+#[cfg(test)]
+mod cancel_tests;
+
 #[cfg(test)]
 mod tests {
     use super::*;
diff --git a/crates/ui-egui/src/files.rs b/crates/ui-egui/src/files.rs
index 6c22c2a..e74b4c5 100644
--- a/crates/ui-egui/src/files.rs
+++ b/crates/ui-egui/src/files.rs
@@ -676,9 +676,12 @@ impl ModelApp {
         );
     }
 
-    /// Stop waiting for the background job; the model stays as it was.
+    /// Cancel the background job: its command stops at its next check
+    /// ([`fieldcraft_model::progress::check`]) and what it made is dropped; the model stays as
+    /// it was.
     pub fn cancel_loading(&mut self) {
         if let Some(l) = self.loading.take() {
+            l.progress.cancel();
             self.queued.clear();
             for w in &l.waiters {
                 let _ = w.send(json!({"ok": false, "error": format!("cancelled: {}", l.title), "cancelled": true}));
diff --git a/docs/control-protocol.md b/docs/control-protocol.md
index 1056587..a6026df 100644
--- a/docs/control-protocol.md
+++ b/docs/control-protocol.md
@@ -28,7 +28,7 @@ checked and clamped (drag steps, wheel lines, window size); `ui.render` refuses
 | `engine.execute` | `command`: command id, `params`: JSON object, `wait?` (default true) | the command's result; a solve or a mesher runs as a [job](#jobs) |
 | `job.status` | — | `job`: the running job (`title`, `command`, `elapsed` seconds, `progress` `{step: {name, index, count}, stage, done, total}`, `fraction` 0–1 when bounded, `line` as the window shows it), or null |
 | `job.wait` | — | the running job's result when it ends (null `job` when none runs) |
-| `job.cancel` | — | stops waiting for the job (`cancelled`: what it was); the model stays as it was and every request waiting for it gets `{"ok": false, "cancelled": true}` |
+| `job.cancel` | — | cancels the job (`cancelled`: what it was): its solver or mesher stops at its next increment, time step, supernode or refinement pass and what it made is dropped; the model stays as it was and every request waiting for it gets `{"ok": false, "cancelled": true}` |
 | `engine.script` | `commands`: `[{command, params}, …]` | stops at the first error; `journal`: commands that changed the model so far |
 | `engine.commands` | — | every command: `id`, `label`, `params` (the parameter documentation), `schema` (its parameters as JSON Schema) and `requires` (what the session must hold before it runs: `design`, `geometry`, `nodes`, `mesh`, `analysable`, `material`, `step`, `result`, …; `engine.execute` of a command missing one fails without doing anything, naming each missing piece and its toolbar entry) |
 
@@ -132,6 +132,10 @@ files named on the command line go through native file pickers and open in the b
 `mesh.hex.*`) runs it off the window thread, as the Solve button and a mesher form's OK do: the
 window keeps drawing its progress (step, stage and count, elapsed time) with Cancel. The reply is
 the command's result when it ends, however long that takes; with `"wait": false` it is
-`{"job": n}` at once, and `job.status`, `job.wait` and `job.cancel` follow it. One job runs at a
+`{"job": n}` at once, and `job.status`, `job.wait` and `job.cancel` follow it. Cancel (the button
+or `job.cancel`) interrupts the running command: every solver and mesher checks for it at its
+natural points (increments and Newton iterations, time steps, fluid steps, Lanczos blocks, the
+factorization's supernodes, the tet mesher's refinement and improvement passes, the hex meshers'
+attempts) and stops with `cancelled`, leaving the model unchanged. One job runs at a
 time; another long command meanwhile is refused, naming the job. The MCP server's `solve` and
 `mesh` tools wait for the reply.