Abstract: After considering the effects of confining pressure caused by soil gravity on the ultimate resistance,the relationship between the ultimate resistance and the depth of soil is obtained based on Mohr-Coulomb failure criterion,and a hyperbolic function is proposed to describe this relationship.After investigating the characteristics of several types of p-y curves,the hyperbolic p-y curves are adopted.From these curves,the stiffness coefficients of soil are derived,and a non-linear dynamic differential equation is established with its difference solution presented.To facilitate engineering application,a simplified analysis method is proposed,in which the pile is divided into embedded and free segments and the non-linear properties of pile are taken into account by modifying the length of free segments.Numerical example demonstrates the necessity of non-linear analysis and the reliability of the simplified solutions.