A stripper rubber for use in a drilling head to seal against a work string deployable through the drilling head. The stripper rubber is longitudinally restrained to prevent extrusion of the stripper under pressure and to reduce the tensile and compressive stresses on the stripper rubber. One embodiment of the stripper rubber incorporates upper and lower metal rings which are maintained in spaced apart relation by vertical rods thereby allowing radial expansion as tool joints pass through the rubber but prevents inversion of the stripper rubber under pressure. Reinforcing cords added to the stripper rubber increase the longitudinal strength. A second embodiment bonds a stripper rubber into a cylinder which restrains the rubber in the vertical direction. Radial deflection is accomodated by allowing the rubber to flow vertically as a tool joint passes therethrough. Each of the stripper rubbers incorporates an integrally formed drive bushing which facilitates mounting within the drilling head.