A variety of new polymeric materials ranging from soft rubbers to hard, tough, and brittle plastics were prepared from 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. The relationship between the dynamic mechanical properties of the Various polymers obtained and the stoichiometry, the types of soybean oils and crosslinking agents, and the different modified initiators was investigated. The room-temperature storage moduli ranged from 6 x 10(6) to 2 x 10(9) Pa, whereas the single glass-transition temperatures (T-g) varied from approximately 0 to 105 degrees C. These properties were comparable to those of commercially available rubbery materials and conventional plastics. The crosslinking densities of the new polymers were largely dependent on the concentration of the crosslinking agent and the type of soybean oil employed and varied from 74 to 4 x 10(4) mol/m(3). The T-g increased and the intensity of the loss factor decreased irregularly with an increase in the logarithmic crosslinking densities of the polymers. Empirical equations were established to describe the effect of crosslinking on the loss factor in these new polymeric materials. The polymers based on conjugated LoSatSoy oil, styrene, and divinylbenzene possessed the highest room-temperature moduli and T-g's. These new soybean oil polymers appear promising as replacements for petroleum-based polymeric materials.