Within the framework of linear theory, the basic equations of equilibrium of shallow spherical shells are well known in two types-(1) two coupled fourth degree partial differential equations in terms of a stress function and the normal deflection function and (2) three coupled partial differential equa- tions in terms of three displacement functions. Thus the study of vibration for shallow spherical shells even with the neglect of tangential inertia forces demands for the solution of a complicated system of partial diflerential equations with a totality of eighth degree. It has, however, been proved by the author [1], without any extra similifying assumption, that the basic equa- tions of equilibrium for shallow spherical shells can be reduced to the system below in cartesian co-ordinates-in terms of three displacements.