The problem of dynamics analysis for shells of revolution partially filled with an ideal incompressible liquid was reduced to solving the system of singular integral equations. The direct formulation of boundary integral equation method was applied. The authors have elaborated the method of numerical simulation of the process and approved it by comparison of numerical and analytical solutions. They considered the shell vibrations coupled with liquid sloshing in presence of gravity forces. The free vibrations of elastic cylindrical shell were analyzed using the proposed technique.