In this paper, a phenomenological model for the expansion stage of flexible polyurethane foams production is introduced. This model is based on the expansion of a diphasic compressible fluid (quasi-Ihomogeneous liquid/gas mixture). Expansion is illustrated through the evolution of the gas rate in the mixture. Two mechanisms are at the origin of this evolution: difference of pressure between the gas and the liquid, and CO₂ creation in the mixture. The CO₂ creation is considered through an evolution law of the CO₂ production rate. Evolutions of rheological properties are taken from literature. Numerical resolution is based on mixed and space-time finite elements, using a splitting technique to decouple kinematics computation from evolution equations. Validations are performed on two simple tests: free expansion and closed expansion. An industrial case is also considered: molding of an automobile seat in flexible polyurethane foam, showing the importance of the prediction of quality defaults in these parts.