Abstarct: In this research, the buckling load of an axisymmetric elastic cylindrical shell under axial load and external pressure, has been determined analytically and numerically. The equilibrium and stability equations have been derived by the virtual work principle by considering the first order shear deformation theory as the displacement filed. These equations have been converted to the dimensionless form and the perturbation technique has been used for solving the equilibrium equations. The buckling load is the eigenvalue of the stability equations. In addition, the buckling load has been determined numerically by Ansys finite elements software, and it has been compared with the analytical results. Also, the buckling load of this cylinder under combined loads, has been determined. Finally the effects of the geometrical parameters on the buckling load have been investigated.