A unit for pumping fluid, particularly blood, is provided with an enclosure that has two half-shells and an elastic membrane fixed perimetrically to the enclosure in order to divide its space into two parts. One of the half-shells is provided with valves that are located at the opening of two connecting ducts for the intake and delivery of the fluid, and the other half-shell is connected to a line of working fluid that is alternately pressurized and depressurized. The first valve is a disk-shaped sheet made of elastic material. The first valve is in a central position with a support that is fixed to the opening of the first duct for connection to the outside and is suitable to rest at its peripheral region on the support. A second valve is a sheet of elastic material located at the peripheral region of the disk at the opening of the second duct for connection to the outside which lies at the peripheral region of the opening of the first duct.