Stitch-machining the walls of a cylindrical blind cavity (10) of a workpiece (14), the cavity (13) being deep and narrow with respect to the axis of the cavity, is carried out by: (a) supporting a tubular housing (10) for axial movement throughout substantially the axial extent of the cavity interior and in close-fitting tolerance to the walls of the cavity, the tubular housing (10) having a free end; (b) rotationally driving a spindle (23) in the tubular housing (10) for conjoint axial movement with the tubular housing, the spindle (23) extending beyond the housing (10) end for carrying a radially adjustable cutting tool (24); (c) inserting the tubular housing (10) together with the rotationally driven spindle (23) in the cavity (13) with the cutting tool (24) radially positioned for rough boring of the cavity walls, while guiding and steering the tubular housing (10) and spindle (23) to accurately concentrically position the cutting tool (24) with respect to the cavity axis ; and (d) substantially immediately upon the execution of rough boring, withdrawing the tubular housing (10) together with the rotationally driven spindle (23) from the cavity with the cutting tool (24) repositioned for finish boring of the cavity wall during withdrawal.