The uniaxial tensile constitutive models of a crosslinked polymer and plasticizer were established based on the characteristics of the network and plasticization by genetic engineering of materials. The key factors affecting the mechanical properties of the polymer matrix were chosen as the genomes of materials. The constitutive model for the crosslinked polymer network with no plasticizer was related to the molecular characteristics of the ingredients, such as the flexibility of the binder prepolymer, functionalities of the ingredients, as well as the curing parameters. On the basis of the constitutive relation of the crosslinked polymer, the constitutive model for the crosslinked polymer and plasticizer was also related to the volumetric fraction of the plasticizer and the interaction of the binder prepolymer and plasticizer molecules. Within the range of viscoelastic deformation in the tensile test, the viscoelastic characteristics of the network were considered in the model. Numeric results showed that the predicted and experimentally measured stress-strain curves were consistent under uniaxial tensile loading, indicating that the model satisfactorily predicted the stress and strain response.