A geared hydraulic machine destined to function as a pump or a motor, comprising at least a module (1) comprising a body (10) in which two chambers are afforded, which two chambers intersect, and each of which contains a gear (12, 13) which enmeshes with a gear (12, 13) contained in the other chamber, the body (10) having at least an open end that is closed by a cover (20) comprising at least a seating (21, 22) for a support bearing (210, 220) of at least a gear (12, 13) of the gears; the coupling between the body (10) and the cover (20) comprises at least two abutments (23, 24) which are fashioned in one of the body (10) and the cover (20), each of which abutments (23, 24) is housed in a respective sunken seating (16, 17) which is afforded in the other of the body (10) and the cover (20).