diff --git a/crates/eps/src/import/ai/read/ops.rs b/crates/eps/src/import/ai/read/ops.rs
index de12631eb..2fda3dec1 100644
--- a/crates/eps/src/import/ai/read/ops.rs
+++ b/crates/eps/src/import/ai/read/ops.rs
@@ -82,6 +82,14 @@ impl<'a> Reader<'a> {
             // highlight `-- -- angle length Bh`): a NaN keeps the other operands where they are.
             "--" => return self.push(V::Num(f64::NAN)),
             "[" => {
+                // Drop marks that operators have taken off, so `marks` is the open nesting.
+                while self.marks.last().is_some_and(|&m| !matches!(self.stack.get(m), Some(V::Mark))) {
+                    self.marks.pop();
+                }
+                // Arrays nest as deep as their `[`s; dropping a deeper one would overflow the stack.
+                if self.marks.len() >= MAX_DEPTH {
+                    return Err("it has arrays nested too deeply".into());
+                }
                 self.marks.push(self.stack.len());
                 return self.push(V::Mark);
             }
diff --git a/crates/eps/src/import/ai/tests.rs b/crates/eps/src/import/ai/tests.rs
index 6b1e8622d..52248aa1b 100644
--- a/crates/eps/src/import/ai/tests.rs
+++ b/crates/eps/src/import/ai/tests.rs
@@ -54,6 +54,14 @@ fn ruler_units_from_the_header_set_the_documents_units() {
     assert_eq!(read(with_px.as_bytes()).unwrap().doc.units, Unit::Pixels);
 }
 
+#[test]
+fn arrays_nested_past_the_depth_limit_are_refused() {
+    let deep = |n: usize| layer(&format!("{}{} pop", "[".repeat(n), "]".repeat(n)));
+    let nested = |n: usize| read(stream(&deep(n)).as_bytes()).err().is_some_and(|e| e.contains("nested too deeply"));
+    assert!(!nested(200));
+    assert!(nested(100_000));
+}
+
 /// The children of the first layer.
 fn art(doc: &Document) -> Vec<Arc<Node>> {
     doc.layers.first().and_then(|l| l.children()).cloned().unwrap_or_default()