A model is presented to describe flow-induced crystallization in isotactic polypropylene at high shear rates. This model incorporates nonlinear viscoelasticity, compressibility, and nonisothermal process conditions due to shear heating and heat release due to crystallization. Flow-induced nucleation occurs with a rate coupled to the chain backbone stretch associated with the longest mode relaxation time of the polymer melt, obtained from a viscoelastic constitutive model. Flow-induced nuclei propagate in flow direction with a speed related to shear rate, thus forming shish, which increase the viscosity of the material. The viscosity change with formation of oriented fibrillar crystals (known as "shish") is implemented in a phenomenological manner; shish act as a suspension of fibers with radius equivalent to the radius of the shish plus the attached entangled molecules? The model is implemented in a 2D finite element code and validated with experimental data obtained in a channel flow geometry. Quantitative agreement is observed in terms of pressure drop, apparent crystallinity, parent/daughter ratio, Hermans' orientation, and shear layer thickness. Moreover, simulations for lower flow rates are performed and the results are compared, in a qualitative sense, to experiments from literature. (C) 2015 The Society of Rheology.