A CFD approach for extremely nonlinear free surface problems is described. The algorithm is based on the CIP method and the multi-phase computations on wavebody interactions are carried out on a Cartesian grid. Numerical simulation results are presented on the two experiment problems we have conducted. The first is a shipwave interaction problem, and the experiment was carried out using a mathematical ship model in a towing tank. Comparisons between computation and experiment are made on the deformation of the free surface, the pressures on the deck and vertical wall, and the wave-induced motions of the ship. The second is a water entry problem, and the experiment was performed on a circular cylinder dropped from air into a still water surface. Besides this 3-D problem, results on a 2-D water entry problem are also presented for verification of the code.