A series of new shape memory polymers are synthesized by the cationic copolymerization of regular soybean oil, low saturation soybean oil (LoSatSoy oil), and/or conjugated LoSatSoy oil with styrene and divinylbenzene, norbornadiene, or dicyclopentadiene initiated by boron trifluoride diethyl etherate or related modified initiators. The shape memory properties of the soybean oil polymers are characterized by the deformability (D) of the materials at temperatures higher than their glass-transition temperatures (T-g), the degree to which the deformation is subsequently fixed at ambient temperature (FD), and the final shape recovery (R) upon being reheated. It is found that a T-g well above ambient temperature and a stable crosslinked network are two prerequisites for these soybean oil polymers to exhibit shape memory effects. Good shape memory materials with high D, FD, and R values are prepared by controlling the crosslink densities and the rigidity of the polymer backbones. The advantage of the soybean oil polymers lies in the high degree of chemical control over the shape memory characteristics. This makes these materials particularly promising in applications where shape memory properties are desirable.