The use of constitutive equations to describe the electromechanical behavior of electrostrictive materials began over 100 years ago. While these equations have been used to model a host of ceramic-based and polymer-based electroactive materials, a fully characterized model has not yet been developed to predict the response of transversely isotropic polymer electrostrictives. A constitutive model is developed within a thermodynamic and hyperelastic framework that incorporates the transversely isotropic material symmetry that is present in many polymer-based electrostrictives. The resulting constitutive model is characterized for three electrostrictive polymer systems using empirical data that are available in the literature. The model has a relatively simple functional form that is easily adaptable to other polymer electrostrictive material systems.