diff --git a/Tests/Data/Mechanics/CooksMembrane/3D/CooksMembrane_3D.prj b/Tests/Data/Mechanics/CooksMembrane/3D/CooksMembrane_3D.prj
index f5a7b5df838..e669c844a8c 100644
--- a/Tests/Data/Mechanics/CooksMembrane/3D/CooksMembrane_3D.prj
+++ b/Tests/Data/Mechanics/CooksMembrane/3D/CooksMembrane_3D.prj
@@ -193,7 +193,7 @@
         <vtkdiff>
             <file>cooks_membrane_ld_3D_n25_ts_1_t_1.000000.vtu</file>
             <field>sigma</field>
-            <absolute_tolerance>2e-3</absolute_tolerance>
+            <absolute_tolerance>3e-3</absolute_tolerance>
             <relative_tolerance>5e-7</relative_tolerance>
         </vtkdiff>
     </test_definition>