Abstarct: The aim of this study is to present an analytical solution for non-linear elastic analysis of cylindrical and truncated conical thick shells with variable thickness under non-uniform pressure made of hyperelastic materials in quasi-static state. The material of the shell is generally considered as hyperelastic functionally graded isotropic material baxsed on two-term Mooney-Rivlin and neo-Hookean models in nearly incompressible state with radially variation of material properties. The variation of the thickness and pressure profiles of the vessel are considered in axial direction by linear and/or nonlinear functions. As geometry, loading and boundary conditions are symmetric respect to revolution axis of the shell, the axisymmetric condition is considered for the problem. Considering non-linear kinematics (strain-displacement) and constitutive (stress-strain) relations for the shell, the governing equations are derived baxsed on first-order shear deformation theory. The system of nonlinear coupled ordinary differential equations with variable coefficients is solved by the usage of perturbation theory for clamped boundary conditions. By the usage of Matched Asymptotic Expansion (MAE) of the perturbation theory, inner and outer equations along with coefficient matrices and non-homogeneity vectors up to the second-order perturbed expansion are presented. Finally, a composite uniform solution is presented for the components of displacements by the usage of matched and boundary conditions and Cauchy stresses are calculated indirectly baxsed on non-linear kinematics and constitutive relations. In order to validate the results of the current analytical solution, a numerical modeling baxsed on finite element method (FEM) by the usage of ANSYS software is investigated. The results of analytical solution and numerical simulation for cylindrical and truncated conical shells with variable thickness in homogeneous and non-homogenous cases show the convergence of the presented solutions.