The applicability of the Wagner model to numerical flow analyses of the injection molding process is investigated under the following approximations: the strain and stress histories of the molten polymer before the injection is negligible, and the flow field in a mold cavity is treated as Hele-Shaw flow. A comparison between the results for simple step-strain-rate flow calculated with the Wagner model and that calculated with the Leonov model suggests that the Wagner model is superior to the Leonov model for unsteady flow because of its stability and accuracy. Therefore, numerical flow analysis software of a viscoelastic fluid in the injection molding process is developed using the Wagner model. For the analysis, the velocity profile of a Newtonian fluid is used instead of that obtained through iterative calculation. The validity of the developed program is confirmed through a comparison of the results of the computation for two simple flow velocity histories with the analytical results from the Wagner model. Furthermore, the computation time of the developed software is only 1.4 times greater than that of the previous numerical flow analysis of a viscous fluid.