Mining machine (1) for driving tunnels, said mining machine (1) including: a cutting head (5) having rock engaging cutting elements (5´), a rotator (32) for driving said cutting head (5), means for forcing the cutting head against rock to be worked so as to disintegrate the rock, and means (7,7´) for transporting away released material. The cutting head is on an upper side is attached to a one-sided support unit. The mining machine includes a pressing unit arranged to press the cutting head (5) linearly against rock to be worked, and the rotator (32) is arranged to rotate the cutting head (5) in a first rotational direction during a cut where the cutting head is in a first side position and in a second rotational direction in a cut where the cutting head is in a second side position. The invention also relates to a method.