A machine (1) for extracorporeal blood treatment comprises a device (2) for ultrafiltration of a liquid through a semi-permeable membrane (3) of a blood treatment device (4), a first sensor (11) for ultrafiltration rate through the membrane, a second group of sensors (13) for measuring a trans-membrane pressure, an infusion line (16) with an infusion pump (17) and a programmed controller (14) for calculating a maximum infusion rate as a function of the transmembrane pressure. The machine is suitable for kidney failure treatments, such as hemofiltration and hemodiafiltration. In a relatively short time the machine enables a large quantity of corporeal blood to be removed from the patient.