Three-dimensional numerical simulation of solidification of high density polyethylene (HDPE) in a parallelepiped shaped extrudate is accomplished using a cell model for spherulite growth on a microscopic level under quiescent conditions and coupled with an enthalpy based heat transfer equation on the macroscopic level. The parallelepiped is cooled from the melting point of HDPE by a stream of air blown across it. When the thickness of the extrudate is of the order of microns, the distribution of the degree of crystallinity and temperature is uniform, and the lumped system formulation to model crystallization and heat flow is applicable. But significant variations inside the extrudate are observed when the thicknesses are of the order of millimeters and centimeters. The non-dimensional Deborah and Blot numbers are shown to be important in the applicability of the formulation. The effects of air speed and ambient temperature on the crystallization process are also studied. It is observed that both 1) an increase in the air speed and 2) a decrease in the ambient temperature increase the rate of crystallization in the parallelepiped. The former has much greater effect than the latter in changing the average convective heat transfer coefficient. As a result, increasing the air speed results in much larger spherulites compared to reducing the ambient temperature. Decrease of temperatures in the extrudate during the either cooling processes is observed to be non-monotonic owing to the release of the latent heat during crystallization. Introducing a constant temperature (melting point of HDPE) at a cross section of the extrudate changes the distribution of relative crystallinity and temperature in the extrudate significantly: the temperature gradient becomes much higher along the extrudate axis, and the material near the cross section never solidifies. Also, the extrudate behaves more like a fin as the variations in the thickness direction become insignificant.