A new stability investigation method based on normal modes of linearized free-surface perturbations is presented. Stability criteria, for each temporal schemes, are deduced from this method via a symbolic computation of the two eigenvalues of the amplification matrix, allowing us to choose the optimal time step in a straightforward manner. Moreover, efficient semi-implicit schemes well adapted to the BEM simulation of free-surface flow are proposed. They seem to be an innovation in literature. By using this kind of new schemes, stable simulations over large time can be obtained, without any artificial smoothing.