Abstract: The wedging action fixture to which the invention relates has a wedging action means, a pair of pressing members, wedging action releasing means and other members for limiting the relative movement and transmitting forces between these parts. This fixture can be secured to any desired portion of an elongated supporting member by a wedging action performed by the wedging action means. The external force to be borne is applied to the wedging action means so as to obtain a wedging force which is transmitted to a pair of pressing members. The pressing members acts on both surface of the elongated supporting member so as to cramp the latter therebetween or, alternatively, on both opposing walls of a channeled supporting member to urge the walls away from each other, thereby to bear the external force at any desired position on the elongated supporting member.