Products made of polyurethane foam are manufactured by the chemical reaction of various low-viscosity raw materials and additives. The diversity of different formulations to meet the requirements of the market makes the characterization of their processing and flow properties important for a simple and error-free production. The modeling and simulation of such processes are equally of great importance. This provides additional findings without the expense of real tests and makes it easier to design components. The work described in this paper was carried out against this background. An experimental setup using a rheometer was developed to determine the flow and curing properties of reacting polyurethane foam reproducibly with comparable expansion conditions to industrial processes. The experiment was mathematically modelled to investigate the rheology of reacting polyurethane foams. The mathematical framework consists of coupled, non-linear, partial differential equations for the dynamics and the heat transfer processes in the system. These are solved numerically in 3D using finite volume techniques under adequate physical conditions. The accuracy of two viscosity laws according to the state of the art and their novel combination were investigated in this context. The proposed viscosity model of this study provides accurate results compared to the experiment.