The boundary element method is extended to simulate the non-linear sloshing of liquid in a two-dimensional tank. In the proposed method, higher-order element (cubic element) is employed for discretization of the boundary integral equation in order to improve the accuracy of numerical solutions. The details of the boundary element technique are described in reference to formations of cubic element. Several numerical examples are presented for liquid-sloshing in circular and rectangular tanks subjected to forced surge oscillation, and are compared with solutions obtained by the boundary element method with linear element, furthermore, the usefulness of the proposed method is discussed.