Valve structures (100) formed in elastomer material (108) are electrostatically actuated by applying voltage to a flexible, electrically conductive wire pattern. An actuation force generated between the patterned wire structure and an electrode (112) result in closure of a flow channel (102) formed in elastomer material (108) underlying the wire. In one embodiment of a valve structure (100) in accordance with the present invention, the wire structure is patterned by lithography and etching of a copper/polyimide laminate, with an underlying gold plate (114) positioned on the opposite side of the flow channel (102) serving as an electrode (112). In an alternative embodiment (400), application of an actuation force between the first (418) and second (428) patterned strips closes the control channel (422) and an associated flow channel (406) underlying the control channel (422).