A peristaltic pump (1) comprising a pump body (2), an inlet (21), an outlet (22) and a pipe (4) attached to the inlet (21) and to the outlet (22) by a device comprising: —a flange (5) held to the pump body (2) by a bracket (6), —an insert (8), inserted against the inner wall (41) of the pipe (4) and comprising a shoulder (82), the inner wall of which bears against the outer wall (52) of the flange (5), characterised in that the pump body (2) comprises an inner circular groove (23) at the inlet (21) and at the outlet (22), and in that the securing device comprises a deformable elastic ring (10) inserted into said circular groove (23), and a pusher (11) having the shape of a ring comprising a projection matching the shape of the groove, the elastic ring (10) being compressed by the pusher (11).