The method consists of forcing a cleaning solution, such as caustic soda, through an inner passage of the needles (40), then injecting pressurized air into said needles, and afterwards flushing pressurized water through the inside of the needles. The machine comprises upper and lower compartments (2, 3) separated by a tray (6), and a tank (4) for the cleaning solution. The tray (6) supports the needles to be cleaned, such that a lower portion thereof is inside a number of containers (17) from which said needles (40) receive said cleaning solution driven by a pump (29), the pressurized air (23) and the washing water (25), through ducts (19, 21, 23, 25, 27) provided with valves (20, 24, 26, 28) in communication with the containers (17). The tray (6) collects the fluids coming out of the upper holes of the needles (40).
