The presence of an extensive ice‐rich layer in the near subsurface of the Martian regolith could result in viscous creep responsible for softening of craters at middle and high latitudes. The temperature of ground ice will vary spatially within a crater owing to the effect of slope on the effective angle of insolation. The temperature at a particular latitude will also vary temporally owing to changes in Mars' obliquity. Results from numerical simulations of viscous creep indicate that these temperature variations cause the pole‐facing slopes of craters to be systematically steeper than those of equator‐facing slopes. Crater slopes should be most asymmetric between 25° and 40° latitude, depending on the thickness of the creeping layer. This slope asymmetry predicted from theoretical simulations of regolith creep is not well developed in observed Martian crater topography. Mars Orbiter Laser Altimeter (MOLA) topography of craters 16 to 40 km in diameter was analyzed for north‐south slope asymmetry within seven latitude regions ranging from 60°S to 60°N. On the basis of the lack of any systematic slope asymmetry observed in the craters, we can place a conservative upper limit of ∼150 m on the thickness of the ice‐rich creeping layer assuming a volumetric dust content of ≤70% and an exponentially decreasing regolith porosity with depth. If the creeping layer contains relatively clean ice, then the thickness of ice‐rich material is limited to ∼100 m or less. The observations also suggest that the thickness of this creeping layer is reduced by ∼30% toward the equator. These results imply a global ice‐rich regolith water volume of <∼107 km3, comparable to that proposed for a modest‐sized northern plains ocean.