Abstarct: In present study, dynamic analysis and free vibration of thin cylindrical shells are presented. The problem is considered to be axisymmetric and thickness of cylinder is constant. Cylindrical shell is made up of heterogeneous and isotropic material, with variable properties through the axial directin according to the exponential law, and obeys linear elastic constitutive equations. As a common assumption, Poisson’s ratio is supposed to be constant throughout the shell. Equations of motion are derived by using classical thin shell theory. The kinematic of problem is according to the linear strain-displacement relation. The governing equations are derived by using Hamilton’s principle. In frequency analysis, boundary conditions are simply-support and clamp and in dynamic analysis, just simply-support boundary condition are investigated. The cylinder is under moving internal pressure with constant velocity. The governing equations form a coupled system of linear partial differential equations with variable coefficient. The expansion theoy of eigenmodes and modal analysis has been applied to obtain analytical solution. Also, the parametric finite element modeling of the problem is done by using ANSYS Parametric Design Language (APDL).the effects of variations of cylinder’s geometric, heterogeneity and loading parameters upon dynamic response, critical velocity, dynamic loading factor and natural frequencies of the shell are studied. The results are validated and compared with those in literature and those obtained from the finite elements method (FEM).