A method for obtaining an air product from an air separation plant having a distillation column system and a tank system. The tank system includes a first tank and a second tank. Cryogenic liquid is withdrawn from the distillation column system, stored in the tank system, and used as the air product. The cryogenic liquid is supplied to the first tank and withdrawn from the second tank during a first period, and is supplied to the second tank and withdrawn from the first tank during a second period. The tank system has a third tank to which cryogenic liquid withdrawn from the first tank and the second tank is transferred unheated. The air product is withdrawn from the third tank in liquid state, vaporized and discharged. Alternatively, the cryogenic liquid can be withdrawn from the third tank and stored in the liquid state in a fourth tank.