The on-bottom stability of submarine pipeline is a key problem of submarine pipeline design.The key issue is to simulate the interaction among wave,pipe and soil. In this paper, the constitutive models of soil, such as nonlinear elastic, porous elastic and Ramberg-Osgood models are adopted respectively, and the pipe/soil interaction has been analyzed by the common finite element software ABAQUS program. The contact surfaces have been established. The factors such as contact effect, frictional coefficient between pipe and soil, pipe's penetration, the impact of yielding stress are considered. Also, the results show that the computation of the pipe/soil interaction is feasible and may provide a helpful tool for the engineering practice of pipeline on-bottom stability design.