Abstract: Thin shells are prone to fail by buckling due to compressive membrane stress. Although shells develop primarily membrane stresses, in most practical situations, they have some bending stresses as well as a result of supports, loading condition and discontinuity. In such case, the response of a shell to external loads becomes nonlinear. Linearization of the nonlinear equilibrium equations gives rise to an eigen value problem solving which buckling load is obtained. Eigen value buckling analysis is computationally faster than the nonlinear analysis involving tracing the load-deflection path and finding the corresponding collapse load. However, the buckling load estimated using the eigenvalue buckling analysis is approximate and usually overestimated. For the systems with large prebuckling rotations this approach may give highly unconservative results. Attempts have been made for better prediction of actual buckling load of shells of revolutions by combining eigenvalue buckling analysis and geometric nonlinear analysis. Such methods are computationally more efficient than the nonlinear buckling analysis but more reliable than the linear buckling analysis. This study presents an overview of the stability analysis of shells of revolution using a conical frustum shell element incorporating the linear and simplified nonlinear buckling analysis including the treatment of initial geometric imperfection.