The thermally and flow induced crystallization behavior of semi-crystalline polymer in processing can significantly influence the quality of final products. The investigation of its mechanism has both scientific and industrial interest. A mathematical model in three dimensions for thermally and flow induced crystallization of polymer melts obeying differential Phan-Thien and Tanner (PTT) constitutive model has been developed and solved by using the finite element-finite difference method. A penalty method is introduced to solve the nonlinear governing equations with a decoupled algorithm. The corresponding finite element-finite difference model is derived by using the discrete elastic viscous split stress algorithm incorporating the streamline upwind scheme. A modified Schneider's approach is employed to discriminate the relative roles of the thermal state and the flow state on the crystallization phenomenon. The thermally and flow induced crystallization characteristics of polypropylene is investigated based on the proposed mathematical model and numerical scheme. The half crystallization time of polypropylene in a cooled couette flow configuration obtained by simulation are compared with Koscher's experimental results, which show that they agree well with each other. Two reasons to cause crystallization of polypropylene in pipe extrusion process including the thermal state and the flow state are investigated. Both the crystalline distribution and crystalline size of polypropylene are obtained by using the finite element-finite difference simulation of three-dimensional thermally and flow induced crystallization. The effects of processing conditions including the volume flow rate and the temperature boundary on the crystallization kinetics process are further discussed. (C) 2012 Published by Elsevier Ltd.