Abstract: In this paper, the vertical forced vibration of dynamic foundation on viscoelastic layered half space was studied in detail. At first fundamental equations of elastodynamics were solved using the method proposed by the authors and Hankel transform solution of vertical displacement at the surface of layered half space were obtained by using Thomson Hankel Transfer Matrix. Then the dual integral equation of vertical vibration of a rigid body on viscoelastic layered half space was established according to the mixed boundary-valued condition. This dual integral equation was reduced to Fredholm integral equation of the second kind. Numerical examples are given at the end of the paper.