A process is provided for producing semi-rigid polyurethane foams having exceptional shock-absorbing properties, even after repeated compression, prepared by the reaction of a polyisocyanate; a polyether polyol having a molecular weight within the range from about 2,000 to about 10,000; from about 1 to about 5% by weight of water per part by weight of polyether polyol; from about 1 to about 6% by weight of urea and/or thiourea per part by weight of polyether polyol; and a cross-linking compound having at least three active hydrogen atoms per molecule that are reactive with isocyanate groups and having a molecular weight below about 1000 in an amount from about 5 to about 25% by weight per part by weight of polyether polyol; the amount of polyisocyanate being selected to give an isocyanate index within the range from about 0.7 to about 1.4.The process provides polyurethane foams that have a cellular structure that remains undamaged under compression as high as 60% at temperatures within the range from about +60.degree. C to about -40.degree. C, and the consequent deformation is less than 1% even after ten compressions of at lest 50% in rapid succession.Accordingly, the invention further provides vehicle bumpers having an impact-receiving layer of this polyurethane foam, and that meet the requirements of FMVSS 215.