An extension of the finite element method to the stability analysis of shells of revolution under static axisymmetric loading is presented in this paper. A systematic procedure for the formulation of the problem is based upon the principle of virtual work. This procedure results in an eigenvalue problem. For solution, the shell of revolution is discretized into a series of conical frusta. The buckling mode in the circumferential direction is assumed, this assumption makes the problem economical for the computing time. The present method is applied to a number of shells of revolution, under axial compression or lateral pressure, and comparision are made with other theoretical results. The results show good agreement each other. The effects of aspect ratio, boundary conditions and buckling modes on the buckling strength of shells of revolution are studied. Also the optimum shape of cylindrical shell under uniform axial compression is obtained from the view point of structural stability.