The invention relates to a one-shot process for the preparation of cellular or noncellular polyurethane polyurea parts having a modulus of flexural elasticity greater than 600 N/mm.sup.2 and densities of from 0.8 to 1.2 g/cm.sup.3 using the reaction injection molding technique, by reacting organic polyisocyanates, a polyol component, aromatic diamines, additional chain extenders and/or cross-linking agents in the presence of catalysts and optionally blowing agents, auxiliaries and/or additives, wherein the polyol component is a mixture containing(i) from 95 to 60 percent by weight of at least one compound selected from the group consisting of polyols, polyether polyamines, polyesteramides, and their mixtures having functionalities of from 2 to 6 and a molecular weight of from 1000 to 8000 and(ii) from 5 to 40 percent by weight of a least one aromatic and/or aromatic-aliphatic polyester polyol having a functionality of from 2 to 3 and a molecular weight of from 254 to 700, wherein the percents by weight are based on the total weight of the polyol component.