A hemostasis valve comprises a housing defining a passage therethrough adpated to receive an elongated member such as a catheter in hemostatically sealed condition. An elastic gasket valve is carried in the housing having slit means capable of permitting the elongated member to extend through the housing and the gasket member in hemostatically sealed condition. By this invention the gasket member defines a pair of opposed sides with a first slit extending inwardly of the gasket member from one of the opposed sides. A second slit extends inwardly of the gasket member from the other of the opposed sides. Both of the slits are of a shape defining a plurality of radii extending from a common origin. The first and second slits extend inwardly at a depth to engage but not to intersect each other, and the radii of the first slit each define an angle of at least 10.degree. to each of the radii of the second slit at points of engagement. By this, an improved hemostasis valve is provided.