An equilibrium thermodynamic approach is employed to derive a continuum-level expression for the electric field-induced stress in uniaxial anisotropic materials. Although this model is developed specifically to describe electrorheological and electrostrictive behavior of suspensions, it also applies to other uniaxial materials such as nonpolar nematic liquid crystals, biaxially oriented polymer films, and paper. This model introduces new electrostriction coefficients, which are material parameters that describe the strain dependence of the dielectric tensor as well as the field-induced stresses. An experimental technique for measuring the electrostriction parameters is outlined. An idealized microscopic model is presented to illustrate the relationships between microscopic parameters and the macroscopic electrostriction coefficients. The model is used to determine the stresses in common applications; predictions from the continuum approach agree with direct calculations from a microscopic approach of the normal stress and static shear modulus of electrorheological suspensions.