A valve structure comprises an elastomeric block formed with first and second microfabricated recesses separated by a membrane portion of the elastomeric block. The valve is actuated by positioning a compliant electrode on a first side of the first recess proximate to and in physical communication with the membrane. Where the valve is to be electrostatically actuated, a second electrode is positioned on a second side of the first recess opposite the first side. Application of a potential difference across the electrodes causes the compliant electrode and the membrane to be attracted into the flow channel. Where the valve is to be electrostrictively actuated, a second electrode is positioned on the same side of the recess as the compliant electrode. Application of a potential difference across the electrodes causes the electrodes to be attracted such that elastomer membrane portion material between them is compressed and bows into the flow channel. Either of the electrostrictively or the electrostatically-actuated valve structures may include an electrically-conducting fluid in the second recess to serve as the compliant electrode.