A composite velocity procedure for the three-dimensional reduced Navier-Stokes equations is developed. In the spirit of matched asymptotic expansions, the velocity components are written as a combined multiplicative and additive composite of viscous like velocities (U, W) and pseudo-potential or inviscid velocities (phi sub x, phi sub y, phi sub z). The solution procedure is then consistent with both asymptotic inviscid flow and boundary layer theory. For transonic flow cases, the Enquist-Osher flux biasing scheme developed for the full potential equation is used. A quasi-conservation form of the governing equation is used in the shock region to capture the correct rotational behavior. This is combined with the standard nonconservation nonentropy generating form used in nonshock regions. The consistent strongly implicit procedure is coupled with plane relaxation to solve the discretized equations. The composites velocity procedure is coupled with plane relaxation to solve the discretized equations. The composits velocity procedure applied for the solution of three-dimensional afterbody problems.