Modelling of free surface flows of polymeric melts in cold, complex-shaped cavities is an essential part of computer-aided design in injection molding. Such flows are invariably accompanied by wall solidification which, in crystallizing polymers, is followed by crystallization and the development of unique and complex microstructures in the molded part. Given the detrimental effect of microstructure on a range of product properties, there is a need for the development of design models which link the processing history of the material to the morphology of the final product. This article presents a model for the filling stage of injection molding of fast crystallizing thermoplastics such as HDPE, with the focus on the effect of high undercooling on the development of crystallinity in the molded product under conditions of uniform and spatially varying cooling. For this, it is essential to extrapolate crystallization rate data, usually obtained in a narrow temperature range below the melting point, to conditions of high undercooling typical of injection molding. Previous work in this area is reviewed and a model for a rational extrapolation of crystallization rate data to low temperatures is utilized. Simulation results predict the development of a variety of (frequently counter-intuitive) surface crystallinity distributions, depending on the temperature history of different sections of the cavity during filling. Such simulation results provide valuable insight into the crystallization process during mold filling and, if accompanied by reliable material data and cooling rates, can be used to tune the process for the production of parts with tailored property profiles.