A hydrostatic testing tool for testing containers, hoses or the like under high pressures. The testing tool having a coupling that threadably engages a threaded aperture of a test container without having to be rotated into the threaded aperture. The hydrostatic testing tool may be hooked up to a source of pressurized medium and the tool includes a container-engaging head having a plurality of collet segments that each have a threaded surface that can expand radially outward, partially due to the force of the pressurized medium, to engage a threaded aperture of the test container, allowing for the formation of a liquid and/or gas tight seal under high pressures. The testing tool further includes an actuating unit connected to the head that controls the movement of the collet segments with a piston or the like.