Based on the shallow water wave theory, the basic equations to describe the nonlinear responses of sloshing are derived, and a numerical method is presented to simulate sloshing phenomena in a rectangular tank which is oscillated horizontally. As the dispersion relation of the free surface wave plays an important role in the stable calculation of resonant responses, it should thus be taken into consideration. In this study, it is implicitly replaced by the dispersion relation produced by the discretization of the basic equations. Numerical results are in good agreement with those of experiments. In cases of shallow water depths, stable progressive waves are observed both in experiments and in numerical calculations, and the various nonlinear characteristics of sloshing, such as the hardening restoring forces and the jumping phenomena in resonant responses are well-simulated by the basic equations and the calculation method presented in this paper.