Advances in numerical simulation capabilities have made the modeling of both glass-conditioning and glass-forming processes feasible. Glass-forming operations include large free surface deformations, conjugate heat transfer, and complex contact phenomena. In this paper, glass-container forming processes are modeled to provide insight into the impacts of the various stages of forming and conditioning on final container quality. The model uses finite elements and includes the effects of viscoelasticity, surface tension, and time-varying heat transfer. Special attention is given to areas that require further developments in numerical capabilities and an increased knowledge of boundary conditions and material properties.