A new constitutive model with internal structure parameter is presented in this study for simulating orientation and deformation of polymer chain in the post/filing stages of injection molding process. Implementation of such a model is based on a hybrid finite-element/finite-difference numerical solution of the generalized Hele-Shaw flow. The simulation of a compressible viscoelastic fluid under nonisothermal conditions has not yet been discussed in most previous works. In addition to the distribution of pressure, temperature, density, and velocity, theoretical predictions also include shear and normal stresses, which can be used for subsequent calcula-tion of residual stresses. An amorphous material, namely a commercial-grade poly-styrene (PS), was used in the present work. Good agreement is obtained between the simulation and experimental pressure trace from this study.