A boundary element model is used to simulate the problem of nonlinear wave generation, and the interactions of wave and current. The numerical model is established based on the potential wave theory with nonlinearities embedded on the free surface and wave generating boundaries. Constant elements are used in the numerical formulation and an incremental expression is used for nonlinear dynamic analysis. From present computations transients of wave generations can be observed. The present model is further used to calculate the interaction of waves and current. From numerical results, it shows that surface waves eventually climb up the opposing current with an elevated mean water level.