In this paper we consider vibrations of the baffled elastic fuel tank partially filled with a liquid. The compound shell was a simplified model of a fuel tank. The shell is considered to be thin and the Kirchhoff-Love linear theory hypotheses are applied. The liquid is supposed to be an ideal and incompressible one and its flow introduced by the vibrations of a shell is irrotational. The problem of the fluid-structure interaction was solved using the reduced boundary and finite element methods. The tank structure was modeled by the FEM and the liquid sloshing in a fluid domain was described by using the multi-domain BEM. The rigid and elastic baffled tanks of different forms were considered. The dependencies of frequencies via the filling level were obtained numerically for vibrations of the fluid-filled tanks with and without baffles. Keywords: baffles, fluid-structure interaction, free vibrations, liquid sloshing, multi-domain boundary element method, systems of singular integral equations.