An analysis of the steady-state film blowing process based on a two-phase constitutive model that accounts for flow-enhanced crystallization is presented. The amorphous melt phase is represented by a multi-mode Giesekus constitutive equation with a transformation-dependent relaxation time and the semi-crystalline phase is represented by a rigid rod model. The relaxation times in the two constitutive equations are linked by an Avrami, temperature-dependent rate expression which contains a term in the Helmholtz free energy to account for flow-enhancement. Comparisons are made to experimental data for film blowing of linear low density (LLDPE) and low density (LDPE) polyethylenes. Excellent fits for the bubble radius, temperature, and crystallinity are shown. It is also shown that the ratio of amorphous stress to total stress at the "lock-in" point provides an excellent correlating variable-for the elongation to break and yield strength properties of the as-blown-film. Inclusion of multiple relaxation times in the Giesekus model offers insights on the controlling role of the maximum relaxation time in the stress profiles and locking-in behavior due to crystallization.