A system for producing beverages from single-serve capsules, comprising: a capsule comprising a cup-shaped container with an outer annular flange and closed by a lid welded to the flange; a brewing assembly comprising a pressurized water injection assembly and a beverage extraction assembly aligned along an axis and relatively movable between an open configuration, in which the injection and extraction assemblies define a capsule loading space therebetween, and a closed configuration, in which the injection and extraction assemblies are arranged one against the other and define a brewing chamber for the capsule therebetween; the injection assembly comprises a cup which is arranged with a free edge thereof towards the extraction assembly, and is mounted to move between an inoperative backward position and an operative forward position, in which, during operation, the cup houses a capsule and its free edge either engages or is arranged close to the flange; the thickness, measured radially, and a diametral size of the free edge are so sized that the free edge engages the flange only at annular area of the flange arranged close to an outer circumferential edge of the flange, so that said annular area is arranged in a radially outer position to any sealing element of the capsule associated with the flange; characterised in that the extraction assembly comprises a hydraulic cylinder comprising a fixed cylindrical body and a piston, which comprises a head portion facing the injection assembly, and is axially slidably mounted in the cylindrical body to axially slide between a normal backward position and an extracted position, in which, the head portion is compressed against the free edge of the cup arranged in the forward position with an axial force such as to couple the flange and the free edge in a fluid-tight manner; the system for producing beverages further comprises a hydraulic circuit comprising a cold water supply and a supply line (47, 52, 54, 58) that connects the cold water supply to the injection assembly; said supply line (47, 52, 54, 58) comprises a first stretch (47, 52, 54) which extends, in series, starting from the cold water supply, through a pump, the hydraulic cylinder of the extraction assembly, a boiler and a check valve, and a second stretch that connects the check valve to the injection assembly; the check valve is set to open when, during operation, water pressure along the first stretch (47, 52, 54), downstream of the pump, reaches a pre-set threshold pressure. a capsule comprising a cup-shaped container with an outer annular flange and closed by a lid welded to the flange; a brewing assembly comprising a pressurized water injection assembly and a beverage extraction assembly aligned along an axis and relatively movable between an open configuration, in which the injection and extraction assemblies define a capsule loading space therebetween, and a closed configuration, in which the injection and extraction assemblies are arranged one against the other and define a brewing chamber for the capsule therebetween; the injection assembly comprises a cup which is arranged with a free edge thereof towards the extraction assembly, and is mounted to move between an inoperative backward position and an operative forward position, in which, during operation, the cup houses a capsule and its free edge either engages or is arranged close to the flange; the thickness, measured radially, and a diametral size of the free edge are so sized that the free edge engages the flange only at annular area of the flange arranged close to an outer circumferential edge of the flange, so that said annular area is arranged in a radially outer position to any sealing element of the capsule associated with the flange; characterised in that the extraction assembly comprises a hydraulic cylinder comprising a fixed cylindrical body and a piston, which comprises a head portion facing the injection assembly, and is axially slidably mounted in the cylindrical body to axially slide between a normal backward position and an extracted position, in which, the head portion is compressed against the free edge of the cup arranged in the forward position with an axial force such as to couple the flange and the free edge in a fluid-tight manner; the system for producing beverages further comprises a hydraulic circuit comprising a cold water supply and a supply line (47, 52, 54, 58) that connects the cold water supply to the injection assembly; said supply line (47, 52, 54, 58) comprises a first stretch (47, 52, 54) which extends, in series, starting from the cold water supply, through a pump, the hydraulic cylinder of the extraction assembly, a boiler and a check valve, and a second stretch that connects the check valve to the injection assembly; the check valve is set to open when, during operation, water pressure along the first stretch (47, 52, 54), downstream of the pump, reaches a pre-set threshold pressure.