Abstarct: In this research, mathematical analysis of truncated conical shells under transverse load is presented. Equations of motion are derived using Donnell-Mushtari-Vlasov Theory. The kinematic of problem is according to the karman strain-displacement relation and the Hook's law is used as the constitutive equation. These equations which are a system of coupled nonlinear partial differential equations with variable coefficients have been derived by using the Hamilton’s principle. The nonlinear Galerkin method and the homotopy perturbation method (HPM) has been applied to solve the equations. baxsed on this analytical solution, the response of the system and the natural frequencies, are determined for a given set of initial values and boundary conditions. Finally, a parametric study is performed to investigate the effects of the various parameters such as thickness, density, length and semi-vertex angle on the linear and nonlinear natural frequencies.