Homogeneous mixtures of a liquid rubber based on prepolymers of epoxidized soybean oil with amines, diglycidyl ether of bisphenol A epoxy resins, and commercial diamines form, under certain conditions, two-phase thermosetting materials that consist of a rigid epoxy matrix and randomly distributed small rubbery soybean particles (0.1-5 mum). These two-phase thermosets have improved toughness, similar to that of other rubber-modified epoxies, low water absorption, and low sodium content. In comparison to the unmodified thermosets, the two-phase thermosets exhibit slightly lower glass-transition temperatures and Young's moduli, but their dielectric properties do not change. The epoxidized soybean oil is available at a price below that of commercial epoxy resins and appears very attractive for epoxy toughening on an industrial scale.