The hydroelastically coupled oscillations of a liquid and the elastic side walls of a rectangular tank partially filled with a liquid, in response to the lateral excitation, are investigated. It is well-known that there are tow types of liquid motion, i.e., sloshing and bulging. In the present paper, the sloshing motion, in which the liquid surface oscillation may be of finite amplitude, is analyzed taking the nonlinearity into account. The time histories of the liquid surface displacement and the wall deformation are calculated to the harmonic, and earthquake excitations by the modal analysis approach. An experiment was conducted using a model tank, and the vibration responses of a liquid and the walls were measured. A good agreement was found between the theoretical and experimental results.