A new coupling method for solving SSI problems is presented.The method

combining analytical and numerical methods

is based on substructure method.The analytical method obtains a frequency domain solution for an elastic superstructure

rigid foundation

and semi-infinite elastic soil systems.A time domain recursive filter is used to transfer the frequency domain solution to time domain.In the system

the dynamic equation of the boundary force and displacement conditions is built based on the responses of each substructure

i.e.

the soil and the structures. In this paper

the new method is used for analyzing a simple linear elastic dynamic system including a single frame structure and a rigid foundation of elastic semi-infinite soil.The results by the coupling method are compared with those by pure analytical method to verify its accuracy

stability and applicability.