A new exact solution is developed which enables to determine the free vibration characteristics of toroidal thin shell with homogeneous boundary conditions.But the solution requires numerical evaluation of an eight order complex determinant to find its eigenvalues.The results are exact in the same sense as the numerical solution of the transcendental frequency equation for a beam yields an exact solution of its vibration frequency.The eigenvalues of cylindrical shell with the boundary conditions corresponding to simple-simple support(SS)

clamped-free support(CF)and clamped-simple support(CS)have been calculated and their dependences on the slenderness of the shell have been found out yet.The results are compared with those obtained by other investigators using different methods and experiments.