Electrostatic forces play a central role in micro- and nanoelectromechanical systems (MEMS and NEMS) and are integral to the rapidly developing field of microfluidics. In electrostatic-elastic systems the interaction of elastic membranes with static electric fields causes membrane deflection. In microfluidic systems, the interaction of static electric fields with small quantities of fluid leads to droplet motion and breakup. In numerous situations of practical interest, the system may be viewed as an elastic membrane enclosing a finite fixed volume. This volume constraint leads to a modification of the standard equations governing electrostatic-elastic interactions. In this paper the basic equations for an idealized volume constrained system are presented and modifications to the un-constrained solution set discussed.