Mars Orbiter Laser Altimeter (MOLA) topography shows distinct elevation offsets across wrinkle ridges that can be explained simply by subsurface thrust faults. MOLA has provided the first reliable topographic data of wrinkle ridges to test models for their origin; although previous work has shown that wrinkle ridges result from compressional folding and faulting of near-surface units, the role of thrust faulting and its depth penetration have been argued. Topographic profiles across wrinkle ridges in Solis Planum, Lunae Planum, Tempe Terra, Xanthe Terra, Arcadia, Terra Sirenum, Thaumasia Planum, Arabia Terra, Syrtis Major, and Hesperia Planum show characteristic features such as superposed hills, crenulations, and elevation offsets between the plains on either side of the ridge. The characteristic elevation offsets between plains surfaces on either side of the ridges shown by MOLA are easily explained by subsurface thrust faults that underlie the ridges and produce the offset. In Solis Dorsa, wrinkle ridges are 10–20 km wide (well resolved by the 300 m spaced MOLA elevations), have a total relief of 80–250 m, and have elevation offsets of 50–180 m (well above the uncertainty in the MOLA elevations). MOLA topography shows that the plains decrease in elevation toward the southeast and are deformed into folds or arches not visible in images that are parallel to and in between the ridges. The elevations of the plains on either side of the ridges in Solis and Lunae Plana are characteristically down to the southeast and east, respectively, suggesting that faults beneath the wrinkle ridges offset the plains. This offset indicates underlying thrust faults that dip to the northwest and west, respectively, and systematically lower the southeast side of the plains. The observation that the elevation offsets across the ridges are maintained to the next ridge implies that the thrust fault penetrates to depths of tens of kilometers and thus well into the mechanical lithosphere. Small foreland basement uplifts on Earth, in which slip on shallowly dipping thrust faults in the crystalline basement is accommodated by folding in the overlying sedimentary rocks, appear to be broadly analogous to these groups of wrinkle ridges and suggest that they are examples of thick-skinned compressional deformation on Mars. These observations are not consistent with models for the formation of wrinkle ridges that involve folding of near-surface layers only or subsurface thrust faults that flatten into decollements at shallow depths.