A machine (1) for extracorporeal blood treatment comprises a device (2) forultrafiltration of a liquid through a semi-permeable membrane (3) of a bloodtreatment device (4), a first sensor (11) for ultrafiltration rate through themembrane, a second group of sensors (13) for measuring a trans-membranepressure, and a programmed controller (14) for calculating a maximumultrafiltration rate as a function of the transmembrane pressure. The machineis suitable for kidney failure treatments, such as hemofiltration andhemodiafiltration. In a relatively short time the machine enables a largequantity of corporeal blood to be removed from the patient.