Abstarct: In this research, the mathematical and numerical analysis of viscoelastic cylindrical shells with moderately large deflection under moving load are presented. These equation are derived using the Hamilton’s principle baxsed on the classical plate theory. The kinematic of problem is according to the von-Karman strain-displacement relations and the Hook’s law is used as the constitutive equation. The governing equations are a system of coupled nonlinear partial differential equations with constant coefficients. They are solved analytically with the perturbation technique and straight forward expansion method. The response of the system, the critical velocity and the natural frequencies, are determined for a given set of initial values. Finally, a parametric study is performed to investigate the effects of the various parameters such as the thickness, radius, modulus of viscosity and elasticity on the system response, natural frequencies and critical velocity. The results of natural frequencies are compare with the numerical method too.