This disclosure relates to a method and apparatus for clamping electrical conductors, such as cables. The conductors are placed in clamping channels formed in a clamp body having at least two separate body parts. The channels have a cross-sectional shape deviating from the circular shape of the conductors. When the clamp is pressed together by means of a pressing tool, the body parts bend elastically about the conductors, while the conductor metal deforms to the shape of the clamping channels. The clamp is then secured by at least one screw of required tensile strength sufficient only to absorb the elastic forces of the deformed body parts and conductors.