Abstarct: In this thesis, the buckling load of homogenous and isotropic cylindrical shell with varying thickness is determined analytically by considering the initial imperfection. The outer radius is constant and the inner has linear variations. The displacement field is defined by using the first order shear deformation theory. The strain-displacement relations are determined by applying the von-Karman relations and the constitutive equations obey the Hook’s law. The shell is axisymmetric and it is subjected to constant axial and variable external pressures. The equilibrium equations are extracted using the virtual work principles. The equations which are a system of nonlinear ordinary differential equations with variable coefficients are solved by using the perturbation technique. The stability equations are derived by two different methods and they are solved analytically. Also, the effect of initial imperfection which is assumed as an initial radial displacement, on the buckling load is investigated. The results are compared with the finite element method and some other references. The presented method for solving the equations, is capable to investigate the behavior of shell with different profiles of thickness and different external pressures. The boundary conditions are considered clamped and simply supported. By using perturbation technique the axial and radial displacements are extracted with a high accuracy even near the boundaries. The initial imperfection can also affect buckling load. In addition, the first order of shear deformation theory is more appropriate for determining the buckling load of thicker shells.