The microstructure model of Doufas and McHugh [J. Rheol. 45, 1085-1104 (2001)] for film blowing of low density polyethylene which uses a modified Giesekus constitutive equation with conformation tensor for the melt and the rigid-rod model with an orientation tensor for the semicrystalline phase is investigated in this study. It is compared with the continuum model describing the melt with a multimode Giesekus equation and the semicrystalline phase as a modified Hookean solid. The phase transition in both models is governed by the crystallization which in the case of the microstructure model affects the relaxation times of the two phases. The comparison of the two models illustrates similarities, but also distinct differences. The bubble geometry and velocity calculated with the two models are almost the same. The orientation tensors determined for the two models also follow a similar evolution. The two models predict very different stresses in the semicrystalline phase during the transition. The microstructure model forecasts stresses in the semicrystalline phase starting from zero when crystallization begins. The continuum model uses the stresses in the melt as the starting point for the stresses in the semicrystalline phase. This seems to be more realistic and is the reason why the continuum model is favored for future investigations. (C) 2018 The Society of Rheology.