This paper deals with the computer simulation of those aspects of Reactive Injection Molding (RIM) dealing with the non‐isothermal and transient flow of a chemically reacting mixture into a mold cavity, and the in situ polymerization (“curing”) which follows mold filling. Linear polyurethane systems were considered. The purpose of this simulation work is to investigate the effects of the operating, chemical, and rheological variables on the length and the stability of the RIM process, as well as the quality of the resulting product. Since the flowing fluid mixture is reactive, there is a need to know the thermal history of each of the flowing fluid particles. For this reason the “fountain” flow at the fluid‐air interface is considered in a heuristic fashion.