This paper deals with the fluid-structure interaction analysis of a shell partially filled with a liquid. The shell is considered to be thin and the Kirghoff-Lave linear theory hypotheses are applied. The liquid is ideal and incompressible. The problem of analysing the dynamics of shells of revolution partially filled with an ideal incompressible liquid was reduced to solving the system of singular integral equations. The solution was obtained by using a coupled BEM and FEM in-house solver. The tank structure is modelled by the FEM and the liquid sloshing in the fluid domain is described by the BEM. The shell vibrations coupled with liquid sloshing under the force of gravity were considered. The shell and sloshing modes were analysed simultaneously. The free vibration analysis of the elastic cylindrical shell was carried out using the proposed techniques. Keywords: fluid-structure interaction, liquid sloshing, free vibrations, boundary and finite element methods, systems of singular integral equations.