This article proposes a generalized Newtonian model to predict the three-dimensional gas penetration phenomenon in the GAIM process, where the gas and melt compressibility are both taken into account and hence the primary and secondary penetrations in GAIM processes are able to be quantitatively predicted. Additionally, an incompressible model requiring no outflow boundary is also presented to emphasis the influence of gas compressibility on the primary penetration. Based on a finite volume discretization, the proposed numerical model solves the complete momentum equation with two front transport equations, which are employed to track the gas/melt and air/melt interfaces. The modified Cross-WLF model is adopted to describe the melt rheological behavior. The two-domain modified Tait equation is exploited to represent the melt compressibility, while a polytropic model is employed to express the gas compressibility. The proposed schemes are quantitatively validated by the gas penetration characteristics in a clip-shaped square tube, where good prediction accuracy is obtained. The influences of five major molding parameters, such as the injection pressure, mold temperature, melt temperature, delay time, and melt material on the gas penetration characteristics in the same clip-shaped square tube via the proposed numerical approach are extensively presented and discussed.