Non-linear wave motion on the free water surface in a two-dimensional container subjected to external periodical excitation is considered in this paper. In order to analyse the problem for arbitrary container geometries, a solution scheme using free surface Lagrangean particles is employed. Fluid motion is assumed to be governed by the Laplace equation in terms of the velocity potential with a non-linear pressure equation on the surface. The boundary element method with explicit time marching is used by the fluid region boundary discretization alone at each time increment. Various containers with an inclined side wall are analysed for the horizontal sway motion and compared.