Machine suitable for cryotherapy treatment of a zone of a human or animal body, the machine comprising: - a tank of liquid having an inlet and an outlet, - a hydraulic pump having a liquid suction inlet and a liquid delivery outlet, which pump is situated upstream of the tank, - a liquid refrigeration unit, which unit comprises an inlet and an outlet, - a pressurized closed hydraulic circuit comprising: ∘ a third hydraulic line connecting the outlet of the tank to the inlet of the pump, ∘ a fourth hydraulic line connecting the outlet of the tank to the outlet of said circuit, ∘ a fifth hydraulic line connecting the inlet of said circuit to the inlet of the pump, ∘ an outlet via which the cooled liquid circulates towards a wrap suitable for being fitted onto the zone that is to be treated, ∘ an inlet via which the liquid returns from the wrap, - a control unit controlling the speed of the pump on the basis of pressure signals emitted by pressure sensors installed in the hydraulic circuit, characterized in that: - the pump is the only hydraulic pump connected to the hydraulic circuit, - the refrigeration unit is situated outside of the tank, which refrigeration unit comprises an inlet and an outlet, - the hydraulic circuit comprises: ∘ a first hydraulic line connecting the outlet of the pump to the inlet of the refrigeration unit, ∘ a second hydraulic line connecting the outlet of the refrigeration unit to the inlet of the tank, - at least one expansion vessel (61, 610) for absorbing the variations in pressure and/or in volume of the liquid in the hydraulic circuit is incorporated into said circuit, - the control unit controls the speed of the pump on the basis of pressure signals emitted by the pressure sensors installed in the hydraulic circuit and/or on the basis of flow rate signals emitted by at least one flow meter installed in said hydraulic circuit. - a tank of liquid having an inlet and an outlet, - a hydraulic pump having a liquid suction inlet and a liquid delivery outlet, which pump is situated upstream of the tank, - a liquid refrigeration unit, which unit comprises an inlet and an outlet, - a pressurized closed hydraulic circuit comprising: ∘ a third hydraulic line connecting the outlet of the tank to the inlet of the pump, ∘ a fourth hydraulic line connecting the outlet of the tank to the outlet of said circuit, ∘ a fifth hydraulic line connecting the inlet of said circuit to the inlet of the pump, ∘ an outlet via which the cooled liquid circulates towards a wrap suitable for being fitted onto the zone that is to be treated, ∘ an inlet via which the liquid returns from the wrap, ∘ a third hydraulic line connecting the outlet of the tank to the inlet of the pump, ∘ a fourth hydraulic line connecting the outlet of the tank to the outlet of said circuit, ∘ a fifth hydraulic line connecting the inlet of said circuit to the inlet of the pump, ∘ an outlet via which the cooled liquid circulates towards a wrap suitable for being fitted onto the zone that is to be treated, ∘ an inlet via which the liquid returns from the wrap, - a control unit controlling the speed of the pump on the basis of pressure signals emitted by pressure sensors installed in the hydraulic circuit, - the pump is the only hydraulic pump connected to the hydraulic circuit, - the refrigeration unit is situated outside of the tank, which refrigeration unit comprises an inlet and an outlet, - the hydraulic circuit comprises: ∘ a first hydraulic line connecting the outlet of the pump to the inlet of the refrigeration unit, ∘ a second hydraulic line connecting the outlet of the refrigeration unit to the inlet of the tank, ∘ a first hydraulic line connecting the outlet of the pump to the inlet of the refrigeration unit, ∘ a second hydraulic line connecting the outlet of the refrigeration unit to the inlet of the tank, - at least one expansion vessel (61, 610) for absorbing the variations in pressure and/or in volume of the liquid in the hydraulic circuit is incorporated into said circuit, - the control unit controls the speed of the pump on the basis of pressure signals emitted by the pressure sensors installed in the hydraulic circuit and/or on the basis of flow rate signals emitted by at least one flow meter installed in said hydraulic circuit.