Abstract: Anexact analytical solution was presented for free vibration of composite shell structure-hermetic capsule. The basice quations on axisymmetric vibration were based onthe Love classical thin shell theory and derived for shells of revolution with arbitrary meridian shape. The conditions of the junction between the spherical and the cylindrical shell segments are givenby the continuity of deformation and the equilibrium relations near the junction point. The mathematical model of problem is reduced to as an eigenvalue problem for a system of ordinary differential equations in two separate domains corresponding to the spherical and the cylindrical shell segments. By using Legendre and trigonometric functions, exact and explicitly analytical solutions of the mode functions were constructed andthe exact frequency equation were obtained. The implementation of Maple programme indicates that all calculations are simple and efficient in both the exact symbolic calculation and the numerical results of natural frequencies compare with the results using finite element methods and other numerical methdos. As a benchmark, the exactly analytical solutions presented in this paper is valuable to examine the accuracy of various approximate methods.