diff --git a/python/mujoco/rollout.cc b/python/mujoco/rollout.cc
index e591af34..2bb4dbcf 100644
--- a/python/mujoco/rollout.cc
+++ b/python/mujoco/rollout.cc
@@ -75,10 +75,11 @@ void _unsafe_rollout(std::vector<const mjModel*>& m, mjData* d, int start_roll,
                      const mjtNum* state0, const mjtNum* warmstart0,
                      const mjtNum* control, mjtNum* state, mjtNum* sensordata) {
   // sizes
-  int nstate = mj_stateSize(m[0], mjSTATE_FULLPHYSICS);
-  int ncontrol = mj_stateSize(m[0], control_spec);
-  int nv = m[0]->nv, nbody = m[0]->nbody, neq = m[0]->neq;
-  int nsensordata = m[0]->nsensordata;
+  size_t nstate = static_cast<size_t>(mj_stateSize(m[0], mjSTATE_FULLPHYSICS));
+  size_t ncontrol = static_cast<size_t>(mj_stateSize(m[0], control_spec));
+  size_t nv = static_cast<size_t>(m[0]->nv);
+  int nbody = m[0]->nbody, neq = m[0]->neq;
+  size_t nsensordata = static_cast<size_t>(m[0]->nsensordata);
 
   // clear user inputs if unspecified
   if (!(control_spec & mjSTATE_CTRL)) {
@@ -92,7 +93,7 @@ void _unsafe_rollout(std::vector<const mjModel*>& m, mjData* d, int start_roll,
   }
 
   // loop over rollouts
-  for (int r = start_roll; r < end_roll; r++) {
+  for (size_t r = start_roll; r < end_roll; r++) {
     // clear user inputs if unspecified
     if (!(control_spec & mjSTATE_MOCAP_POS)) {
       for (int i = 0; i < nbody; i++) {
@@ -128,7 +129,7 @@ void _unsafe_rollout(std::vector<const mjModel*>& m, mjData* d, int start_roll,
     }
 
     // roll out trajectory
-    for (int t = 0; t < nstep; t++) {
+    for (size_t t = 0; t < nstep; t++) {
       // check for warnings
       bool nwarning = false;
       for (int i = 0; i < mjNWARNING; i++) {
@@ -141,7 +142,7 @@ void _unsafe_rollout(std::vector<const mjModel*>& m, mjData* d, int start_roll,
       // if any warnings, fill remaining outputs with current outputs, break
       if (nwarning) {
         for (; t < nstep; t++) {
-          int step = r*nstep + t;
+          size_t step = r*static_cast<size_t>(nstep) + t;
           if (state) {
             mj_getState(m[r], d, state + step*nstate, mjSTATE_FULLPHYSICS);
           }
@@ -152,7 +153,7 @@ void _unsafe_rollout(std::vector<const mjModel*>& m, mjData* d, int start_roll,
         break;
       }
 
-      int step = r*nstep + t;
+      size_t step = r*static_cast<size_t>(nstep) + t;
 
       // controls
       if (control) {
@@ -226,7 +227,8 @@ mjtNum* get_array_ptr(std::optional<const py::array_t<mjtNum>> arg,
   py::buffer_info info = arg->request();
 
   // check size
-  int expected_size = nbatch * nstep * dim;
+  size_t expected_size =
+    static_cast<size_t>(nbatch) * static_cast<size_t>(nstep) * static_cast<size_t>(dim);
   if (info.size != expected_size) {
     std::ostringstream msg;
     msg << name << ".size should be " << expected_size << ", got " << info.size;
diff --git a/python/mujoco/rollout_test.py b/python/mujoco/rollout_test.py
index f27dc02b..f2b5358f 100644
--- a/python/mujoco/rollout_test.py
+++ b/python/mujoco/rollout_test.py
@@ -16,6 +16,7 @@
 
 import concurrent.futures
 import copy
+import os
 import threading
 
 from absl.testing import absltest
@@ -25,7 +26,6 @@ import numpy as np
 import mujoco
 from mujoco import rollout
 
-
 # -------------------------- models used for testing ---------------------------
 
 TEST_XML = r"""
@@ -875,6 +875,26 @@ class MuJoCoRolloutTest(parameterized.TestCase):
             model, [copy.copy(data) for i in range(3)], initial_state, control
         )
 
+  @absltest.skip(reason='Takes a long time to run')
+  def test_large_state(self):
+    model = mujoco.MjModel.from_xml_string(TEST_XML)
+    nstate = mujoco.mj_stateSize(model, mujoco.mjtState.mjSTATE_FULLPHYSICS)
+    data = mujoco.MjData(model)
+
+    nthread = os.cpu_count()
+    nbatch = nthread
+
+    nstep = ((2**31) // (nstate * nbatch)) + 2
+    assert nstep * nstate * nbatch > 2**31
+
+    initial_state = np.random.randn(nbatch, nstate)
+    rollout.rollout(
+        model,
+        [copy.copy(data) for _ in range(nthread)],
+        initial_state,
+        nstep=nstep,
+    )
+
 
 # -------------- Python implementation of rollout functionality ----------------