In this paper, a numerical analysis of stresses and displacements in FGM thick-walled cylindrical pressure vessel under internal pressure has been presented. The elastic modulus is assumed to be varying along the longitude of the pressure vessel with an exponential function continuously. The Poisson’s ratio is assumed to be constant. Whereas most of the previous studies about FGM thick-walled pressure vessels are on the basis of changing material properties along the radial direction, in this research, elastic analysis of cylindrical pressure vessel with exponential variations of elastic modulus along the longitudinal direction, under internal pressure, have been investigated. For the analysis of the vessel, the stiffness matrix of the cylindrical pressure vessel has been extracted by the usage of Galerkin Method and the numerical solution for axisymmetric cylindrical pressure vessel under internal pressure have been presented. Following that, displacements and stress distributions depending on inhomogeneity constant of FGM vessel along the longitudinal direction of elastic modulus, are illustrated and compared with those of the homogeneous case. The values which have been used in this study are arbitrary chosen to demonstrate the effect of inhomogeneity on displacements and stress distributions. Finally, the results are compared with the findings of finite element method -FEM-.

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