The transducer has a case which is formed by a support frame for supporting a fluid-conducting flow tube and by a case cap for encasing at least one bent segment of the flow tube which vibrates during operation of the transducer. The case cap comprises a channel-shaped first cap segment with a circular-arc-shaped first segment edge of predeterminable radius R and with an essentially identically shaped second segment edge. The first cap segment has a circular-arc-shaped cross section with a radius r less than the radius R of the first segment edge. The case cap further comprises an essentially plane second cap segment, which is connected via a circular-arc-shaped first segment edge with the first segment edge of the first cap segment, and a third cap segment, which is essentially mirror-symmetric with respect to the second cap segment and which is connected via a circular-arc-shaped first segment edge with the second segment edge of the first cap segment. The second and third segments each have a substantially greater flexural rigidity than the first cap segment. The use of the case cap permits the case of the transducer to be made as pressure-resistant as possible at minimum cost.