A razor head has blade members with straight front cuffing edges which are mutually parallel and lie in a cutting plane. Imaginary median surfaces of the blade members are continuously curved from the cutting plane, from the cutting edges toward the rear edges. The razor has a handle with a pair of fork arms, the distal ends of which are connected to the head at positions adjacent the respective ends of the head. Each fork arm has a groove allowing pivoting of the distal end about a pivot axis parallel to the head axis but which does not pass through the razor head. Each groove is filled with a resiliently deformable material which is deformed when a pivoting force is applied to the razor head during shaving and which restores the razor head to a normal position when the force is removed.