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The research of composite load-deformation relationship of soil under vertical and lateral loads is the difficulty in vehicle terramechanics field now. The lateral load causing slide sinkage was put forward by some scholars in the past but the numerical relationship between lateral load and slide sinkage was not clear yet. The deformation law of soil under vertical and lateral loads was analyzed on the base of finite element theory. Firstly, the soil stress-strain characteristics was analyzed and the modified drucker-prager cap model was chosen as the constitutive model of soil considering the soil elastic behavior, yield criterion, hardening law, flow rule and failure criterion. Then the load-deformation relationship of soil under vertical load was analyzed in the way of relationship between plate sinkage and pressure by the plate-sinkage test. Finally, the composite load-deformation relationship of soil under vertical and lateral load was analyzed considering the lateral load influence by the shear test on the base of load-deformation relationship of soil under vertical load. The lateral load could cause the increase of sinkage in the vertical direction, divided the total sinkage into static load sinkage and slide sinkage, it can be found that the lateral load can cause the slide sinkage and there was a linear relationship between shear displacement and the slide sinkage. The influence factors to the value of slide sinkage were analyzed and the major factors that affected the value of sinkage were vertical load and soil plastic parameters such as soil cohesion and frication angel, the soil elastic parameters such as elastic modulus and passion ratio had little effect on the value of sinkage. The linear relationship between shear displacement and slide sinkage of soil was clearly put forward and it can be used to calculate the soil bearing characteristics more accurately in vehicle terramechanics and other research fields involved soil deformation.