Abstract: A valve for medical use has a cannula mounted on a hub and fixed in a fluid conduit so that the cannula points upstream. An elastomeric valve element is mounted on the hub within the conduit so as to enclose the cannula. The valve element has a first solid frustoconical portion upstream of the cannula point, a second hollow frustoconical portion within which the cannula point is disposed, and a third hollow cylindrical portion surrounding the cannula downstream from its point and fixed to the hub. The second portion has a frustoconical interior passageway tapering inwardly from the first portion toward the hub. A supplementary metallic frustoconical sleeve is fixed within the second element interior so as to open outwardly toward the first element and enclose the cannula point. In one type of use, the valve element is compressed to cause the cannula point to pierce the first portion to provide a path for fluid flow through the conduit.