A case (330) for a vibrating meter (300) is provided. The case (330) includes a first panel (331a) defined by at least a first edge (333) and a second edge (334). The case (330) also includes one or more indentations (332) formed in the first panel (331a). The one or more indentations (332) include at least a portion extending from the first edge (333) to the second edge (334). The resonant frequencies of the case can be increased and separated from the intended drive frequencies of the fluid conduits (306A, 306B).