Abstract: A peristaltic pump wherein an annular internal surface of the housing and a sleeve-like annular section of an elastically deformable diaphragm define an annular pumping chamber which communicates with the fluid-admitting inlet and with the fluid-discharging outlet of the housing. The diaphragm is provided with an extension which projects radially outwardly from the sleeve-like section and is partially anchored in a socket of the housing. A weakened portion of the extension between the anchored portion and the sleeve-like section is received in a compartment between the inlet and outlet of the housing and is provided with one or more empty or fluid-filled cavities, with one or more recesses, with one or more holes and/or other elasticity enhancing features to ensure that the resistance of the sleeve-like section to deformation will be uniform in each of its parts including that which is integral with the extension.