The cationic copolymerization of regular soybean oil, low-saturation soybean oil (LoSatSoy oil), or conjugated LoSatSoy oil with styrene and divinylbenzene initiated by boron trifluoride diethyl etherate (BF3. OEt2) or related modified initiators provides viable polymers ranging from soft rubbers to hard, tough, or brittle plastics. The gelation time of the reaction varies from 1 x 10(2) to 2 x 10(5) s at room temperature. The yields of bulk polymers are essentially quantitative. The amount of crosslinked polymer remaining after Soxhlet extraction ranges from 80 to 92%, depending on the stoichiometry and the type of oil used. Proton nuclear magnetic resonance spectroscopy and Soxhlet extraction data indicate that the structure of the resulting bulk polymer is a crosslinked polymer network interpenetrated with some linear or less-crosslinked triglyceride oil-styrene-divinylbenzene copolymers, a small amount of low molecular weight free oil, and minor amounts of initiator fragments. The bulk polymers possess glass-transition temperatures ranging from approximately 0 to 105 degreesC, which are comparable to those of commercially available rubbery materials and conventional plastics. Thermogravimetric analysis (TGA) indicates that these copolymers are thermally stable under 200 degreesC, with temperatures at 10% weight loss in air (T-10) ranging from 312 to 434 degreesC, and temperatures at 50% weight loss in air (T-50) ranging from 445 to 480 degreesC. Of the various polymeric materials, the conjugated LoSatSoy oil polymers have the highest glass-transition temperatures (T-g) and thermal stabilities (T-10). The preceding properties that suggest that these soybean oil polymers may prove useful where petroleum-based polymeric materials have found widespread utility.