Abstract: Based on the differential equation of shear-beam lateral free vibration and the up-right cantilever shear-beam model on a rigid half space, a spring-shear beam model is developed and the implicit analytic solution and recursion formula for single and random multi-layer site are derived, considering the elasticity of a half space. The influence to the calculation results of site natural frequency in the rigid half space assumption is analyzed by the spring- shear beam model. Results show that the error of calculation caused by rigid half space assumption decreased with the increase of modulus ratio and soil thickness. For common practice sites, if the covering layer thickness is not very small, there will be a good calculation precision using traditional shear beam method with a rigid half space.