In order to achieve a better simulation and feedback control performance for legged robot on the soft terrain surface with fluidity, an interaction mechanical model between the robotic single-legged system and the sand (as a soft terrain environment) is proposed, in which some assumptions in ultimate bearing capacity theories from conventional soil mechanics are discussed and inherited. After expansion and deepening of it, the interaction mechanics models of rigid and soft feet with the sand are established, respectively. Compared with other models, the proposed model comprehensively considers the shape characteristics of the interaction surface and the sliding surface, and its parameters are the commonly-used well-measured physical parameters, which means the online identification process is no longer necessary. Finally, a mobile platform of the robotic single-legged system is designed, machined, and established. The experiments of the single-legged system interacting with the sand are carried out in both quasi-static and dynamic impact collision states. Comparison between the experimental results and the simulation predictions shows that the total error between the prediction results and the sampling data is 8.97%. Not only the accuracy of the plastic contact mechanics model is verified, but also the validity of the mechanical behaviour prediction of the foot-terrain contact deformation.