Abstract: By the introduction of two displacement functions,the non-axisymmetric free vibrations of a complete thin isotropic spherical shell submerged in a compressible fluid medium are successfully investigated.It is found that there are two classes of free vibrations:the first class is not affected by the ambient fluid while the second is.It is further proved that the frequency equations can be expressed in terms of polynomial.For the second class of vibration of submerged spherical shell,it is also demonstrated t...