The invention relates to a ground-working machine (11) equipped with a drive and with advancement members (21). Its advancement members (21) serve inter alia to carry a supporting structure (23) set apart from the positioning plane of the machine, on which supporting structure (23) there is arranged, in the region of a central axis (Z), a kirving tool (25) with at least one transverse kirving roller (13) for working a substrate on which the ground-working machine is standing. The kirving roller (13) is rotatable about its roller axis (V). The roller axis (V) is pivotable about a steering axis (W), which steering axis (W) is arranged in the direction of the central axis (Z) set apart from the advancement members (21).