Abstract: Based on the viscoelasticity theory,the general partially differential vibration equation is deduced for the viscoelastic beam on the viscoelastic foundation at first.Then,the method to analyze the free vibration of the foundation beam is put forward under circumstances neglected to the viscosity of the beam,but considering the viscosity of the foundation.This method adapts to the general linear foundation which is composed of N-standard linearity by means of series connection or/and parallel connection,and can be used more widely to analyze complicated structures,such as underground railway tunnel,whose compelled vibration induced by moving train.After this,the results are deduced in detail of an elastic beam on a 3-parameter standard linear foundation subjected to arbitrary boundary conditions and to arbitrary initial conditions.In the end,a numerical analyatic example is given to illustrate the validity of this method.The example shows that with the technique which separating one variable into two,the sequence converges so rapidly that,in ordinary cases,only two series should be taken to meet the requirements of a project.