The invention relates to a rotary sliding vane machine (1) for fluid processing, comprising a housing (2) with a cavity (4) with a rotor (9). Vanes (12) are arranged in outwardly directed slots (13) in the rotor (9), and relative sliding between the vanes and the rotor provides spaces with variable volumes in the rotational direction. Each vane is supported by a vane bearing apparatus (102) comprising a slide bearing body (105) with a slot (13) forming a slide bearing for the vane (12), and a cylindrical convex face (116) facing away from the slot (13), and, on each side of the slot (13), a pivot bearing pad (106) with a cylindrical concave face (117) facing the slide bearing convex face (116), forming a pivot bearing for the vane.