The machine has at least one fluid chamber (20) from which fluid can be discharged under pressure through multiple hollow needles (26). The fluid needles have flow control valves connecting them to the fluid chamber. A control (32) adjusts the valve in dependence on the needle movement. The valves (28) are fitted to a removable or retractable cover (24) mounted on the fluid chamber. The valve for each needle can include a valve needle (28) extending coaxially to each injection needle.