A tunnelling machine has a swing unit (31) that is swingable about a horizontal axis (I). The swing unit has a head (50) that rotates about an axis (II) that is transverse to said horizontal axis and passes the horizontal at a distance below the horizontal axis. The head is equipped with a plurality of disc-cutters (53-58, 63) that are arranged to have their cutting edges on an imaginary sphere with a radius of about the same length as the swing radius. Upon simultaneous upward swinging of the swing unit and rotation of the head, the cutters cut both when on the leading side of the head and when on the trailing side. No cutting occurs during the return swing stroke. When the swing unit has been returned, the machine is advanced a step which is somewhat larger than the distance between the two axes, and another upward cutting stroke can be effected.