The evolution of the spherulitic morphology, commonly encountered during the solidification of semicrystalline materials, is modeled by taking into account the transport of the solute (the noncrystallizing species) and the crystallization kinetics. In this paper, a microscopic cell model is presented that incorporates the influence of these phenomena. The growth of the spherulite in the cell is represented by defining three concentric zones within the unit cell : a liquid zone, a dendritic zone, and a solid zone. The governing equations that describe the process are solved simultaneously with an integral method and a time-stepping scheme to obtain a description of the growth of a spherulite within the cell. Five dimensionless parameters are identified that affect the cooling profile and the microstructure. Also, the concentration profiles of the noncrystallizing species, the cooling history of the spherulite, and the evolution of the grain envelope and the dendritic zone are calculated during the solidification process. These results are obtained for boundary conditions of prescribed heat flow, prescribed cooling rate, and isothermal crystallization. The development of a significant interdendritic region is observed under prescribed heat now, along with the rise in temperature associated with the self-heating of the polymer due to the latent heat. No interdendritic region developed with the prescribed cooling rate, and a much smaller one appeared under isothermal conditions. The solid fraction, in the last case, also reached a plateau below unity due to the choice of cooling conditions. These results are consistent with experimental observations.