The invention relates to water blown integral skin polyurethane foams made with a particular isocyanate quasi-prepolymer and resin side ingredients to yield a foam having good overall mechanical properties. The isocyanate quasi-prepolymer component of the present invention comprises from 0.5 weight percent to 30.0 weight percent or less uretonimine-carbodiimide-modified diphenylmethane diisocyanate, from 50 weight percent to 80 weight percent 4,4'-diphenylmethane diisocyanate and reacted with from 15 weight percent to 40 weight percent of a polyether polyol containing predominately secondary hydroxyl groups and having an average molecular weight from about 2,000 to 10,000, an average functionality from 1.5 to about 3.2, and a hydroxyl number from about 20 to 60, and optionally with a low molecular weight diol in an amount of from 1.0 weight percent to 10 weight percent, the weight percentages based on the weight of the quasi-prepolymer reactants. The resin side component comprises a high molecular weight polyether compound having isocyanate reactive hydrogens and average molecular weights from about 2,000 to about 10,000 and an average functionality from 1.5 to about 3.2, water as a blowing agent in an amount of from 0.25 weight percent to 3 weight percent, an effective amount of polyurethane and/or polyurea promoting catalyst, a surfactant, and a chain extender, and optionally a mono- or di- functional alcohol composition having from 8 to about 30 carbon atoms.The components, when injected or poured into a preheated mold, can tolerate mold temperatures from 105.degree. F. to 135.degree. F. and can be demolded in less than 150 seconds to yield an integral skin foam having little or no bubbles or pores visible to the eye. The foam produced thereby has a compression set of 30 percent or less, high tensile strength, and high tear strength.