Long sublinear ridges and related scarps located at the base of large volcanic structures are frequently interpreted as normal faults associated with extensional regional stress. In contrast, the ridges bordering the Central Costa Rica volcanic range (CCRVR) are the topographic expression of hanging wall asymmetric angular anticlines overlying low‐angle thrust faults at the base of the range. These faults formed by gravitational failure and slumping of the flanks of the range due to the weight of the volcanic edifices and were perhaps triggered by the intrusion of magma over the past 20,000 years. The thrust fault underlying Alajuela ridge rises from a depth of ∼700 m at a dip of ∼15° over a distance of a few kilometers. It ramps up at ∼600 m depth on a ∼40° slope and terminates in the axis of the forward syncline, ∼400 m below the surface. The hanging wall of this fault has been thrusted about 200 m away from the volcanic range axis. Thrusting on the lower flanks of the CCRVR is compensated by extension on the range axis with formation of summit grabens. Shallow seismicity in the volcanic range suggests that thrusting is still active. We postulate that at Kilauea volcano, Hawaii, the gravity‐ and magma‐induced slumping of the southern flank on low‐angle thrust faults generates hanging wall anticlines similar to those observed in Costa Rica. These anticlines are hypothesized to occur along the base of the volcano, where the thrust faults ramp up toward the sea bottom. Ridges and scarps between 2000 and 5000 m below sea level are interpreted as the topographic expression of these folds. We further suggest that the scarps of the CCRVR and Kilauea are valid scaled terrestrial analogs of the perimeter scarp of the Martian volcano Olympus Mons. We suggest that the crust below Olympus Mons has failed under the load of the volcano, triggering the radial slumping of the flanks of the volcano on basal thrusts. The thrusting would have, in turn, formed the anticlinal ridges and scarps that surround the edifice. The thrusting seems to be preferential toward the northwest and southeast, and a northeast‐southwest rift zone seems to have developed, perpendicular to the regional topographic gradient. The thrust faults may extend all the way to the base of the Martian crust (about 40 km), and they may have been active until almost the end of the volcanic activity. We suggest that gravitational failure and slumping of the flanks of volcanoes is a process common to most large volcanic edifices. In the CCRVR and at Kilauea this slumping of the flanks is a slow intermittent process, but it could evolve to rapid massive avalanching leading to catastrophic eruptions. Thus monitoring of uplift and displacement of the folds related to the slump tectonics could become an additional effective method for mitigating volcanic hazards.