Thin revolved shells are intersetted in many engineering applications, in particular dubbly curved shells. In this research, linear and nonlinear buckling analyses (with consideration of geometrical non-linearity) are performed on two different types of elliptical shells known as Oblate and Prolate which are under external hydrostatic pressure. These shells are made of homogeneous steel. ABAQUS (a well-known finite element software) is used for performing the simulations. Several important parameters affecting the buckling behaviour of these revolved elliptical shells are investigated in detail such as the ratio between minor and major radii, the percentage of nonlinear buckling value and the shell thickness magnitude on buckling load capacity. The results show the significant effect of shell geometrical dimensions, the magnitude of nonlinear buckling value as an initial imperfection and the shell thickness variations on the buckling load capacity. Finally, it is also observed that the Oblate shell results in a remarkable reduction in the load capacity compared to the other shell type used in this study. To verify the validity of the results, a comparison is made between the present FEM results and the available theoretical studies and a good agreement is observed.