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In this paper a thick cylindrical shel with varying thicknes which is subjected to static non-uniform internal presure is analyzed. At first, equilibrium equations of the shel have been derived by theenergy principle and by considering the first order theory of Mirsky-Herrmann which includes transverseshear deformation. Then the governing equations which are, a system of diferential equations withvarying coeficients have been solved analyticaly with the boundary layer technique of the perturbationtheory. In spite of complexity of modeling the conditions near the boundaries, the method of this paper isvery capable of providing a closed form solution even near the boundaries. Displacement predictions arein a good agreement with the calculated finite elements and other analytical results. The convergence ofsolution is very fast and the amount of calculations is les than the Frobenius method.