The finite element method (FEM) is used to simulate the penetration process of a pipe pile and the stress of the soil mass around the pile changing with depth is simulated and analysed. Pile driving is a highly nonlinear process and large deformation problems can hardly be solved by a common method by contacting and meshing. Those problems can be solved by ALE meshing technology and a “zipper-type”method. In this paper, the penetration process of an open-ended pipe pile with diameter of 2.134 m into clay soil is investigated by ABAQUS. And the following installation methods are considered: pile jacking and impact driving. The horizontal stress of the soil mass inside the pipe pile is higher than that of the soil mass outside according to the soil stress inside and outside the pile changing with the depth in the pile penetration process. So, soil plugging appears in the pile jacking more easily than that in the impact driving and squeezing effect is relatively obvious. By analyzing the stress changing with time at some points in the soil mass around the pipe pile during the driving, the increase of the stress of the soil mass around the impact pile is lager than that in the pile jacking, and so is the sphere of influence in the soil mass around the pipe pile. Therefere, this effect should be taken into consideration to evaluate the bearing capacity of the pipe pile.