Abstract: The attempt of the present paper is to extend the application of the shell theory to the pressure vessel under a modified working condition. The case treated here is about a mid-thick walled pressure vessel with a large centrally-holed cover of a ellipsoidal shape and the vessel is under working pressure. In the proceeding of the calculation, the cover is divided transversely into two parts and each part is treated separately. The angular deformation produced by the membrane strain was studied for the upper part while the element of the ring strip of a torus was studied for the under. The calculated values obtained checked well with what the experiments give.