The invention relates to a Coriolis mass flowmeter (1) which has at least one curved measuring tube (2), at least one oscillation generator (3), at least one oscillation sensor (4), at least one measuring device electronics (5) and a housing (6). To provide the housing (6) with increased pressure resistance, in particular against external positive pressure, the housing (6) has a first housing shell and a second housing shell, the first housing shell and the second housing shell completely surrounding the measuring tube (2) so as to form at least a first pressure-resistant hollow space around the measuring tube (2), and the first housing shell and the second housing shell forming a bridge (13) between the inlet (10) and the outlet (11) of the measuring tube (2).