A numerical method has been developed for computing the steady state flow about arbitrary shaped three dimensional bodies on or below the free surface using a Boundary Integral Element Method ( Panel Method). The method uses a singularity distribution over the body surface and the free surface. The method can solve for the potential distribution as well as the source density distribution. In this study a constant source distribution is assumed on each panel. The free surface boundary condition is linearized about the uniform undisturbed flow (Kelvin Free Surface condition). Upstream waves are prevented by the use of an one-sided upstream 4-point finite difference operator for the free surface condition. Wave elevations are computed using the linearized free surface condition. In this study two different bodies were considered: a submerged spheroid and a sphere. The wave resistance was computed for different Froude numbers and compares well with existing results. The study has also analyzed the effect of the number of panels on the body surface, the length of the free surface paneling behind the body and the aspect ratio of the free surface panels. / Master of Science