A three-point-contacting pliers for breaking glass along a prescored line has two opposing movable jaws. One jaw has a central projection. To provide an easy exact alignment of the three points of the closing jaws on the prescored line the other jaw, formed as an abutting member or anvil, is provided with a protruding flexible elastic circular ring which may be locked in a receptacle portion and which surrounds the central projection when the jaws are closed. To make alignment of the jaws on the prescored line even easier, the other jaw with the ring may be provided with a throughgoing hole coaxial with the ring which acts as a viewing window and which widens conically from the side of the jaw having the ring.