Electrostrictive materials such as lead magnesium niobate (PMN) are currently being evaluated for use in high-powered sonar transducers and actuators. The principal characteristics which differentiate them from piezoelectric ceramics are nonlinear dependence of the strain on the applied electric field and saturation of the polarization at high electric fields. A new set of constitutive relations for the behavior of electrostrictive materials in one dimension is developed, using the stress and the electric field as the independent variables. These relations are derived from a Gibbs free energy function using thermodynamic definitions of the strain and the electric displacement. The nonlinearity of the strain and the saturation behavior are included explicitly in the formulation. The resulting equations reduce to the correct power series forms for a pure electrostrictor [G. H. Blackwood and M. A. Ealey, Smart. Mater. Struct. 2, 124--133 (1993)] in the limit of small fields and/or stresses. The theory will be shown to be consistent with experimental data on PMN obtained at NUWC. Comparisons with other electrostrictive material models, such as those using polarization as the independent variable [C. L. Hom and N. Shankar, J. Intell. Mater. Syst. and Struct. 5, 795--801 (1994)], will also be made.