Abstract: A rotary peristaltic pump comprises a rotor member (4) fitted in a stator member (5) and coupled to a motor (2) and having a cylindrical head section (6) housing a plurality of pump tube compressing idler rollers (7) equidistantly radially disposed around the head section, with their longitudinal axes parallel to the axis of the head section. The rollers are positioned in an annular recess (8) in the periphery of the head section, the root periphery of the recess being grooved (17) to accept each compressing idler roller such that a substantial part of each roller protrudes into the annular recess. The stator member (5) comprises a base section (9) and wall section (10) defining an axial opening (11) to accommodate the cylindrical head section and has pump tube entry ports (12, 13) in the wall (10) for tangential communication with the annular recess. Stator member (5) may slide along the rotor shaft (31) to facilitate service to the rotor elements and tube.