Abstract: This paper is concerned with the free vibration analysis of conical shell on the two-parameter elastic foundation. By introducing displacement function,U(u,θ,t), the basic partial differential equations in terms of displacements are tranformed into an eight-order partial differential equation. The analytical solution of the governing equation is obtained using a power series method. As an application of the theory, the characteristic equation is derived for the conical shell with the one edge clamped and the other edge simply supported. The numerical results for the winkler model and the two-parameter model are compared in details with the change of the depth of foundation. The applicability of winkler model is addressed.