The present study attempted to numerically simulate the process in detail by developing an appropriate physical modeling and the corresponding numerical analysis for injection molding and injection/compression molding processes of center-gated disks. In Part I, a physical modeling and associated numerical analysis of injection molding with a compressible viscoelastic fluid model are presented. In the distribution of birefringence, the packing procedure results in the inner peaks in addition to the outer peaks near the mold surface, and values of the inner peaks increase with the packing time. Also, values of the density in the core region increase with the packing time. From the numerical results, we also found that birefringence becomes smaller as the melt temperature gets higher and that it is insignificantly affected by the flow rate and the mold temperature. As far as the density distribution is concerned, mold temperature affects the distribution of density especially near the wall. But it was not significantly affected by flow rate and melt temperature. Numerical results of birefringence coincided with experimental data qualitatively, but not quantitatively.