Vibration problems in engineering have got tremendous importance now-a-days. Shells belong to the most useful class of structures and as such, their dynamic behaviour is definitely worth investigating. The basic equations of equilibrium or of motion of shallow shells’ consist of two coupled fourth degree partial differential equations in terms ofa stress function and the normal deflection function. These equations were used by Nowacki’ to study the free vibration of shallow spherical shells. The Marguerre’ equations as well can be used suitably for shells rectangular in ‘plan. These equations of motion of a shell element consist of three equations in terms of three displacement fU11.Etions u, v, w. As such, in solving the system it will be required to use all the three equatIOns simultaneously. It has, however, been proved by the. author’, without any simplifying assumption, that the basic equations of equilibrium (and hence of motion) for a shallow spherical shell can be simplified to the system