Abstract: A pump (1) with one or more pistons (3; 103; 203; 303; 403), which can be rotated, especially for conveying essentially liquid media, the piston (3; 103; 203; 303; 403), having at least regionally a surface layer (17; 117; 217; 317; 417) of a polymer, especially of an elastomer, is constructed so that at least one recess (19; 119; 219; 319; 419), into which a supporting body (20; 120; 220; 320; 420) can be introduced for expanding the polymer layer (17; 117; 217; 317; 417), is assigned to the polymer layer.