The production of molded polyurethane foam products having a compact surface by foaming inside molds is known in principle (for example, German Auslegeschrift No. 1,196,864). It may be carried out, for example, by introducing a reactive and foamable mixture based on compounds containing several hydrogen atoms which are reactive with isocyanate groups and polyisocyanates into a closed mold. The blowing agents used in the processes known in the art are water and/or fluorinated hydrocarbons. Catalysts of the type known for the production of polyurethane foams are also generally used. By suitable choice of the starting components, in particular the choice of the molecular weight and functionality of the components from which the foam is obtained, it is possible to obtain either elastic or rigid foams or any variations between these two types. The dense outer skin is obtained in this process by introducing into the mold a larger quantity of foamable mixture than would be required for completely filling the mold under conditions of unrestricted foaming. The internal wall of the mold generally cools the reaction mixture in contact with it and causes condensation of the organic blowing agent which is preferably used, with the result that the expanding reaction comes to a standstill in the region of the internal wall of the mold so that a compact outer skin is formed. When employing this known method, it was often observed that the viscosity of the foaming reaction mixture increased too rapidly before completion of the foaming process so that the mold did not become completely filled. Another disadvantage of the known process was that the density was not homogenously distributed in the resulting molded foam product. If the reaction mixture foamed vertically in a mold, the density of the foam in the higher part of the mold was much lower than in the lower part of the mold. This is also due to a too rapid increase in the viscosity before termination of the foaming process.