Abstract: A tensioning device includes a tensioning frame having stretcher bars disposed in parallel pairs and displaceable relative to one another, on which bars the edges of a piece of fabric can be clamped. Each stretcher bar has two cooperating clamping devices which extend over the entire length of the stretcher bar, each device being formed by a tube of elastic material adapted to be pneumatically or hydraulically pressurized. Each tube is held in aligned grooves in a closed row of longitudinally movable runners. The clamping force obtained through pressurization acts at every point over the entire length of the clamped edge of the piece of fabric. The elongation of the tubes, which can be increased by gradually raising the pressure, follows the stretching of the piece of fabric during the tensioning operation. The runners move apart during this process, but without losses of tension occurring because of the resulting gaps. Uniform tensioning of the pieces of fabric in line with the threads is thus possible.