Abstarct: In this research, the dynamic response of a viscoelastic thick cylindrical shell under moving load has been evaluated. The material properties obey a viscoelastic model in shear and elastic in bulk. Boundary conditions in both of side of shell is clamped. The first-order shear deformation theory (FSDT) has been assumed as the displacement field. By considering the first standard linear solid model, the governing equations of motion have been derived with the Hamilton’s principle by using the operator method. The governing equations, which are a system of partial differential equations, have been solved analytically and the displacements have been compared with the finite element method (FEM). A code in Ansys package has been prepared for numerical analysis. The analytical solution has been obtained using the Laplace transform and the perturbation technique .baxsed on this solution the effects of the parameters such as damping and moving load velocity on system response have been investigated.