diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index f36591741..fd6407541 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -88,6 +88,19 @@ jobs:
         run: sudo apt-get install libopenblas-dev gfortran
       - run: ./scripts/all-tests.sh "$FEATURES" ${{ matrix.rust }}
 
+  miri:
+    runs-on: ubuntu-latest
+    name: miri
+    steps:
+      - uses: actions/checkout@v4
+      - uses: dtolnay/rust-toochain@nightly
+        with:
+          components: miri
+      - uses: Swatinem/rust-cache@v2
+      - name: Install openblas
+        run: sudo apt-get install libopenblas-dev gfortran
+      - run: ./scripts/miri-tests.sh
+
   cross_test:
     #if: ${{ github.event_name == 'merge_group' }}
     runs-on: ubuntu-latest
diff --git a/ndarray-rand/tests/tests.rs b/ndarray-rand/tests/tests.rs
index 2db040310..4dc4760dd 100644
--- a/ndarray-rand/tests/tests.rs
+++ b/ndarray-rand/tests/tests.rs
@@ -57,6 +57,7 @@ fn oversampling_without_replacement_should_panic()
 }
 
 quickcheck! {
+    #[cfg_attr(miri, ignore)] // Takes an insufferably long time
     fn oversampling_with_replacement_is_fine(m: u8, n: u8) -> TestResult {
         let (m, n) = (m as usize, n as usize);
         let a = Array::random((m, n), Uniform::new(0., 2.));
@@ -84,6 +85,7 @@ quickcheck! {
     }
 }
 
+#[cfg_attr(miri, ignore)]
 #[cfg(feature = "quickcheck")]
 quickcheck! {
     fn sampling_behaves_as_expected(m: u8, n: u8, strategy: SamplingStrategy) -> TestResult {
diff --git a/scripts/miri-tests.sh b/scripts/miri-tests.sh
new file mode 100644
index 000000000..e4480db78
--- /dev/null
+++ b/scripts/miri-tests.sh
@@ -0,0 +1,21 @@
+#!/bin/sh
+
+set -x
+set -e
+
+# We rely on layout-dependent casts, which should be covered with #[repr(transparent)]
+# This should catch if we missed that
+RUSTFLAGS="-Zrandomize-layout"
+
+# General tests
+cargo miri test -v --no-default-features
+cargo miri test -v -p ndarray -p ndarray-rand --lib --tests
+
+# BLAS tests
+cargo miri test -p ndarray --lib -v --features blas
+cargo miri test -p blas-mock-tests -v
+cargo miri test -p blas-tests -v --features blas-tests/openblas-system
+cargo miri test -p numeric-tests -v --features numeric-tests/test_blas
+
+# Examples
+cargo miri test --examples