The hydrodynamic problem of a cone entering the water surface through the free-fall motion has been analysed based on velocity potential theory. The fluid is assumed incompressible and the gravity effect has been ignored. The three dimensional (3D) problem is solved in the cylindrical coordinate system. Axisymmetric flow field is assumed, which has reduced the problem virtually to a two dimensional (2D) one, although the governing equation is no longer Laplacian. The boundary element method is used at each time step. The auxiliary function method has been adopted to decouple the motion of the cone from the fluid flow. Calculated results are compared with those published previously, both from simulation and based on experiments, and good agreement is found. Further simulations are made to investigate the effects of deadrise angle.