A time-dependent viscoelastic model of thermal stress in Martian ice-rich permafrost is developed to test the hypothesis that small-scale polygonal features observed from orbit and by the Viking Lander 2 are the result of thermal contraction cracking, as commonly occurs in terrestrial permafrost. Results indicate that significant tensile stress occurs in Martian ice-rich permafrost as a result of seasonal cycles in the ground temperature. Using conservative rheological parameters appropriate for ice at low temperatures, tensile stresses poleward of about 20¿ to 30¿ latitude easily exceed the tensile strength (assumed to be 2 to 3 MPa) and fractures should readily form. In the equatorial regions, special conditions may allow tensile stresses to approach the tensile strength. These results support a thermal contraction origin of observed small-scale polygonal features and emphasize the utility of these features as valuable morphological indicators of ground ice.¿ 1997 American Geophysical Union