Abstract: Tooling lathe with programmable tool displacement. The lathe of the invention comprises, visible from the outside, a frame with body complete (1), a bench (3) supporting the movable headstock (4), a movable saddle (5) and a fixed headstock supporting a mandrel (7). The movable equipment (5) mounted on the saddle comprising essentially a tool holder (10), a couple of control cranks (13, 14) for dressing and traversing, a handling device (15) with five positions of which one is a central stop position, a display screen (18) and a control desk (20); a push button (16) allows to apply at each depression a feed demultiplication coefficient; a pair of push buttons (17) controls the running or stopping of the lathe; the lathe is characterized in that all control and monitoring members are carried by the movable equipment (5). Application to the turning of unitary parts and parts in small series.