A wire cut electric discharge machine provided with a machining fluid supply apparatus capable of supplying machining fluid in an amount large enough to permit a stable wire extension even in a finishing operation. During rough machining, a first flow regulating valve (6) provided in a first pipe (3) and a second flow regulating valve (10) and an on-off valve (11) respectively provided in a second pipe (4) are fully opened, so that machining fluid is injected from upper and lower nozzles (5, 9) respectively connected to these pipes. In the finishing operation, openings of the first and second flow regulating valves are reduced. When wire extension is carried out, the on-off valve in the second pipe is fully closed, and an on-off valve (7) provided in a bypass pipe (8) and fully closed during both the rough machining and the finishing operation is fully opened, whereby an amount of machining fluid large enough to reliably guide a wire electrode is injected from a jet nozzle connected to the bypass pipe and attached to the upper nozzle, regardless of the opening of the first flow regulating valve which varies between the rough machining and the finishing operation.