diff --git a/crates/engine/src/cmd/modify.rs b/crates/engine/src/cmd/modify.rs
--- a/crates/engine/src/cmd/modify.rs
+++ b/crates/engine/src/cmd/modify.rs
@@ -789,6 +789,9 @@ fn join_point(a: &Segment, b: &Segment) -> Option<Vec2> {
 fn run_offset(s: &mut Session, p: &Value) -> Result<Value> {
     let h = targets(s, p)?.first().copied().ok_or_else(|| bad("offset", "`handle` is required"))?;
     let dist = f64_req("offset", p, "distance")?;
+    if dist == 0.0 {
+        return Err(bad("offset", "Requires a positive distance."));
+    }
     let side = point_req("offset", p, "side")?;
     let e = s.doc()?.entity(h).map(|e| (**e).clone()).ok_or_else(|| bad("offset", "no such object"))?;
     let k = offset_kind(&e.kind, dist.abs(), side).ok_or_else(|| bad("offset", "cannot offset that object"))?;
diff --git a/crates/engine/src/tests.rs b/crates/engine/src/tests.rs
--- a/crates/engine/src/tests.rs
+++ b/crates/engine/src/tests.rs
@@ -344,6 +344,15 @@ fn fillet_two_lines() {
     assert!(g.iter().any(|p| p.near(Vec2::new(2.0, 0.0), 1e-9)));
 }
 
+#[test]
+fn offset_zero_distance_is_rejected() {
+    let mut s = Session::new();
+    s.execute("line", &json!({"points": [[0, 0], [10, 0]]})).unwrap();
+    let r = s.execute("offset", &json!({"handle": "100", "distance": 0, "side": [1, 1]}));
+    assert!(r.is_err(), "offset distance 0 made a coincident copy: {r:?}");
+    assert_eq!(s.doc().unwrap().model.len(), 1);
+}
+
 #[test]
 fn offset_circle_and_polyline() {
     let mut s = Session::new();