A numerical model able to simulate polymer crystallization under nonisothermal flows is developed. It is based on the assumption that the trace of the extra-stress tensor, calculated according to a viscoelastic multimode Upper Convected Maxwell (UCM) model, is the driving force of the flow-induced extra nucleation. Two distinct sets of Schneider equations are used to describe the growth of thermally and flow induced nuclei. The model is then coupled with the momentum equations and the energy equation. As an application, a shear flow configuration between two plates (Couette flow) is simulated. The relative influence of the mechanical and thermal phenomena on the crystallization development as well as the final morphology distribution is then analyzed as a function of the shearing intensity and the cooling kinetics, in terms of nucleation density and crystallite mean sizes. POLYM. ENG. SCI., 50:2044-2059, 2010. (C) 2010 Society of Plastics Engineers