This report describes in detail a computational method for the solution of the partially-parabolic (or semi-elliptic or parabolized) Reynolds-averaged Navier-Stokes equations for the calculation of external flow around ship-like three-dimensional bodies. Among the main features of the method are the following. Numerically-generated body-fitted coordinates are used to facilitate applications to a wide variety of shapes. The convective-transport equations are discretized using the finite-analytic scheme which employs analytic solutions of the locally-linearized equations. A time-marching algorithm is employed to enable future extensions to be made to handle unsteady and fully-elliptic problems. A two-step global pressure-correction algorithm has been developed to accelerate convergence. The method can be used with large solution domains in order to capture the viscous-inviscid interaction.