Reinforced cellular or noncellular molded polyurethane parts are prepared by heating a mixture of reinforcing materials and a heat-curable composition of polyisocyanates and polyols in an open or closed mold, said composition being storage-stable at room temperature and containing, optionally, auxiliaries and additives. In said composition, the polyisocyanate is dispersed in the form of discreet particles having particle diameters from 0.1 to 150 .mu.m in the polyol and the polyisocyanate particles are deactivated on their surfaces such that from 0.01 to 20 equivalent percent of the total available isocyanate groups are deactivated and such that the ratio of free isocyanate groups to hydroxyl groups is from 0.7:1 to 2.5:1.The polyurethane molded parts are suitable for use as self-supporting trim parts, reinforcement parts, or molded parts for various applications.