The present invention provides vascular introducer sheaths incorporating improved passive valves which can maintain hemostasis around medical instruments. A passive sheath valve for creating a hemostatic seal around a medical instrument comprises a valve body having an upstream end, a downstream end, and a lumen having an inner and outer surface therethrough. The valve body defines a sealing aperture that is configured nominally to remain open. The upstream end includes an upstream annulus region defining at least one opening and the downstream end includes a downstream annulus region. Each annulus region and lumen outer surface define at least one chamber. The at least one opening transmits pressure from the upstream end through the upstream annulus region so as to allow a fluid to enter the at least one chamber.