In the last decade,the computational modelling of flows with moving boundaries or free surfaces using FEM and/or BEM has become a topic of great interest in literature,wherein the BEM models are shown to be morL efficient than FEM,particularly for the time-marching scheme and nonlinear iteration algorithm.However,in most of the existing works,the unsteady sloshing problem is considered for 2-D rectangular tanks so that the elevation of the free surface is defined by only one geometric parameter.In this paper,a Lagrange-wise BEM scheme is applied to fit the arbitrary tank and it will be much easier to be extended to the 3-D case and incorporated into the structure'interaction,for which the finite deformation of the tank wall should be taken into account.The numerical results for both rectangular and semi-circular tanks are presented.