Vegetable oils are very heterogeneous materials with a wide distribution of triacylglycerol structures and double-bond contents. The hydrogenation of epoxidized soybean oil (ESO) produces polyols having a functionality distribution related to that of soybean oil. Therefore, these polyols are convenient substances for studying the impact of structural heterogeneity on network formation and properties. Polyols of hydroxyl numbers ranging from 225 to 82 mg KOH/g and weight-average functionalities ranging from 4.4 to 2.7 were obtained by the variation of the time of hydrogenation of ESO. An analysis of the functionality distribution in polyols shows that gel points with diisocyanates vary from 54 to 76% conversion. The molecular weights of the network chains of polyurethanes prepared from these polyols and diphenyl methane diisocyanate varied from 688 to 1993. Polyols with hydroxyl numbers above 200 mg KOH/g gave glassy polymers, whereas those below that value gave rubbers. The heterogeneity of polyols had a negative effect on the elastic properties only at low crosslinking densities. (C) 2007 Wiley Periodicals, Inc.