This paper presents the numerical solutions of slamming problems for 3D bodies entering calm water with vertical and oblique velocities. The highly nonlinear water entry problems are governed by the Navier-Stokes equations and were solved by a constrained interpolation profile (CIP)-based finite difference method on a fixed Cartesian grid. In the computation, the 3D CIP method was employed for the advection calculations and a pressure-based algorithm was applied for the nonadvection calculations. The solid body and the free surface interfaces were captured by density functions. For the pressure computation, a Poisson-type equation was solved at each time step by using the conjugate gradient iterative method. Validation studies were carried out for a 3D wedge, a cusped body vertically entering calm water, and the oblique entry of a sphere into calm water. The predicted hydrodynamic forces on the wedge, the cusped body, and the sphere were compared with experimental data.