For a science-based design of the Powder Injection Molding (PIM) process, it would be desirable for designers to have a numerical analysis tool capable of predicting the PIM filling process as a design aid. In this regard, the present study is aimed at developing a numerical analysis system to simulate the PIM filling process based on a new physical modeling taking into account theological characteristics of powder/binder mixtures, namely the yield stress and the apparent slip phenomena. In particular, two different slip models were employed to represent the apparent slip phenomena. In accordance with the new physical modeling, the numerical simulation of the PIM filling process was accomplished by combining a finite element method and a finite difference method. It was found that the slip layer plays a role of not only a lubricating layer but also a thermal insulation layer. In this aspect, the slip layer model seems to represent the apparent slip phenemena better than the slip velocity model with regard to both the momentum and the thermal transport phenomena. The present paper presents the physical modeling, numerical scheme, and some numerical analysis results showing the effect of the yield stress and slip phenomena.