This paper presents the development of a finite element for the analysis of spherical shells. The derivation of stiffness and mass matrices is based on the improved shell theory which takes into account the effects of rotary inertia and shear deformation. This finite element is then used to determine the natural frequencies and mode shapes for the free axisymmetric vibration case for free, hinged, and fixed boundary conditions. The transient response in the radial direction at the apex of the shell is calculated for shells subjected to time‐dependent internal radial pressures.