Abstract: An abrasive water-jet cutting machine, comprising pumping means, fluidly connectable to a water source, a cutting head, comprising a mixing chamber, a dispensing system of powdered abrasive material, comprising a tank, a supply tube and an actuator interposed between the tank and the supply tube, which delivers the powdered abrasive material contained in the tank into the mixing chamber, through the supply tube; wherein the cutting head mixes, in the mixing chamber, the abrasive material with the water jet forming a water-abrasive material mixture jet, and said cutting head delivers the water-abrasive material mixture jet; wherein the powdered abrasive material delivered into the mixing chamber is homogeneously dispersed in suspension in a water-based gelatinous fluid; and wherein the actuator is a peristaltic pump.