Vise for clamping a pipe or rod or section bar or other mechanical part, with a jaw (3) and a counterjaw (3'), comprising a piston fixed in position by a support (10) with a rod (6) to the head of which said counterjaw (3') is rendered integral through a cart (7); pliers with two catches (9, 9') hinged upon said support (10) to rotate vertically and endowed with hooks (9a, 9a') fit for engaging two corresponding cavities (3a, 3a') provided on respectively upper and lower surfaces of said jaw, said catches having their profile with an inner and outer raising (12, 12a; 12', 12a') toward the exterior of the working field of the pliers themselves, said cart having two pegs (13, 13') respectively fit for engage each one of said outer raisings to cause the closing of the catches with the advancement of the cart by contrast against the outer raisings themselves, and pipe bending machine or rod or section bar bending machine that comprises it, with the jaw being integral with the matrix, as well as comprising a dragging ledge (16) integral with the matrix too, which ledge takes support on the dragging arm in the working sense of rotation, and is idling from it in the return sense, through an adjustable spacer (17).