Legged locomotion has advantages when one is navigating a flowable ground or a terrain with obstacles that are common in nature. With traditional terra-mechanics, one can capture large wheel–terrain interactions. However, legged motion on a granular substrate is difficult to investigate by using classical terra-mechanics due to sharp edge contact. Recent studies have shown that a continuum simulation can serve as an accurate tool for simulating dynamic interactions with granular material at laboratory and field scales. Spurred by this, a computational framework based on the smoothed particle hydrodynamics (SPH) method has been developed for the investigation of single robot appendage interaction with a granular system. This framework has been validated by using experimental results and extended to study robot appendages with different shapes and stride frequencies. The mechanics’ results are expected to help robot navigation and exploration in unknown and complex terrains.