An efficient numerical method for solving the Navier-Stokes equations is extended to allow solution of the equations of the Maxwell and Oldroyd B models of viscoelasticity at moderate Reynolds numbers where inertial terms cannot be ignored. The continuity equation is treated by the artificial compressibility method and the resulting set of equations is split into a hyperbolic set and one that contributes to the mixed character of the system. A flux difference splitting scheme is used to approximate the hyperbolic set and an implicit method is used to time march to steady state. The method is used to solve the channel entry problem. A grid refinement study is done in the entry region of the channel and the solution is matched to a downstream region solution. The latter is compared with the prediction of linear perturbation analysis. Very good agreement is found for the rate of development. Flow over a flat plate is studied and leading edge solutions are qualitatively compared to linear solutions, while the downstream solutions compare well quantitatively with predictions of boundary layer analysis.