A method and rig for driving tunnels, galleries, shafts or the like. The rig has a movable base unit that over a support unit supports a carrying unit which in turn carries a cutting head having outwardly directed cutting elements. The method includes rotating the cutting head around a general axis of rotation and applying the cutting head against a rock surface to be worked. The carrying unit is swung into a first chosen mutual position in respect of the support unit. The support unit is rotated into a second chosen mutual position with respect to the base unit around an axis that is essentially longitudinal with respect to the base unit. An angle of operation of the cutting head is controllable.