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A body-exact computation theory for the large amplitude ship motion using Rankine source Green function has been developed. In contrast to the classical linear theory, the motion amplitude of the body is not restricted while using a linearized free surface boundary condition. The nonlinearity associated with the instantaneous changing geometry of the structure is investigated extensively. By distributing desingularized sources on the free surface and using constant strength panels on the body surface, a boundary-integral formulation is derived. In the zero forward speed problem, an Euler time stepping scheme is used to update the free surface. While, in the case of the three-dimensional forward speed problem, we use an Euler-Lagrange scheme to integrate the free surface boundary condition and update the solution. At each time step, the exact body boundary condition is satisfied. Extensive numerical solutions have been obtained for both two-dimensional and three-dimensional problems. The two-dimensional results include linear computation of the added mass, and damping for a circular cylinder and a box, large amplitude radiation forces of a circular cylinder and a bow flare section of S7-175, and body-exact wave diffraction of a circular cylinder. The two-dimensional water entry and exit problems for a wedge are also studied. Three-dimensional computations include the added mass and damping calculations for a sphere, calm water wave resistance of a submerged spheroid, wave resistance of a Wigley hull, and the radiation force for a modified Wigley hull. Both linear and body-exact radiation computations are shown. Numerical computations are all compared with experiments and other numerical solutions.