An apparatus for making a beverage by infusion of a food substance, the apparatus comprising: - an infusion unit which defines an infusion chamber intended to receive the food substance, the infusion unit comprising a first member and a second member, the first member being movable relative to the second member between a home position, in which the first member and the second member are spaced apart from each other and the infusion chamber is open and allows insertion of the food substance into the infusion chamber or removal of the food substance from the infusion chamber, and an operating position, in which the first member and the second member are coupled to each other and the infusion chamber is closed; - beverage making parts, which are configured to feed, in use, a liquid substance into the infusion chamber, thereby causing the beverage to be made as a result of the interaction between the liquid substance and the food substance; - a dispenser to dispense the beverage, a dispensing duct connecting the infusion chamber to the dispenser; and - a back-pressure valve which is positioned on the dispensing duct and which, based on a pressure difference between an upstream side and a downstream side of the back-pressure valve, prevents or allows a flow of beverage towards the dispenser, the back-pressure valve comprising a sealing seat which surrounds a passage for the beverage, an obturator which is movable relative to the sealing seat between a closed position and an open position, an elastic member which pushes the obturator towards the closed position, wherein in the closed position the obturator is in contact with the sealing seat thereby closing the passage for the beverage and in the open position the obturator is spaced apart from the sealing seat thereby leaving the passage for the beverage open, characterised in that the infusion unit mechanically operates in conjunction with the back-pressure valve by a moving mechanism, in such a way that during the movement of the first member from the operating position to the home position the moving mechanism shifts the obturator from the closed position to the open position and that during the movement of the first member from the home position to the operating position the moving mechanism releases the obturator and allows a return of the obturator to the closed position. - an infusion unit which defines an infusion chamber intended to receive the food substance, the infusion unit comprising a first member and a second member, the first member being movable relative to the second member between a home position, in which the first member and the second member are spaced apart from each other and the infusion chamber is open and allows insertion of the food substance into the infusion chamber or removal of the food substance from the infusion chamber, and an operating position, in which the first member and the second member are coupled to each other and the infusion chamber is closed; - beverage making parts, which are configured to feed, in use, a liquid substance into the infusion chamber, thereby causing the beverage to be made as a result of the interaction between the liquid substance and the food substance; - a dispenser to dispense the beverage, a dispensing duct connecting the infusion chamber to the dispenser; and - a back-pressure valve which is positioned on the dispensing duct and which, based on a pressure difference between an upstream side and a downstream side of the back-pressure valve, prevents or allows a flow of beverage towards the dispenser, the back-pressure valve comprising a sealing seat which surrounds a passage for the beverage, an obturator which is movable relative to the sealing seat between a closed position and an open position, an elastic member which pushes the obturator towards the closed position, wherein in the closed position the obturator is in contact with the sealing seat thereby closing the passage for the beverage and in the open position the obturator is spaced apart from the sealing seat thereby leaving the passage for the beverage open, characterised in that the infusion unit mechanically operates in conjunction with the back-pressure valve by a moving mechanism, in such a way that during the movement of the first member from the operating position to the home position the moving mechanism shifts the obturator from the closed position to the open position and that during the movement of the first member from the home position to the operating position the moving mechanism releases the obturator and allows a return of the obturator to the closed position.