This paper brings into focus some of the interesting effects arising from the motion of the liquid free surface due to sloshing in partially filled containers of several geometrical shapes in two dimensions. The slosh characteristics that include frequencies, free surface profiles and the hydrodynamic pressure over the container walls have been reported in this study. The equations of motion of the fluid, considered inviscid, are expressed in terms of the pressure variable alone. It is assumed that the frequency of the exciting oscillation is not in the immediate neighborhood of the natural slosh frequency, so that the slope of the free surface is small. Simple harmonic oscillation and earthquake excitations are used as the prescribed boundary conditions. A finite difference-based iterative time-stepping technique is employed to advance the solution in the time domain. The paper presents numerical solutions for rectangular, vertically mounted annular cylindrical, trapezoidal and horizontal circular cylindrical containers. Numerical results obtained are compared with the available existing solutions to validate the code developed. The parametric study of the slosh dynamic systems shows the importance of the nature of excitation, fluid height and the geometry of the container. Copyright © 2007 John Wiley & Sons, Ltd.