A mechanism of generating passive feeding flow for the Devonian spiriferide brachiopod Paraspirifer bownockeri was theoretically elucidated through fluid dynamics simulations for flow around rigid shells. The RANS equations were used as a turbulence model, and the unsteady incompressible flow was solved using the finite volume method. Two directions of ventral and dorsal flows were investigated as typical cases where little exchange flow occurs inside the shells. The digital model of the shell was constructed using image processing of X-ray CT images of a shell replica made by molding a polycarbonate plate to a well-preserved fossil specimen of Paraspirifer. To examine the effect of flow velocity, three conditions of ambient flow velocity were adopted for both the ventral and dorsal flows. The pressure distribution along the gape showed that a relatively high pressure occurred around the sulcus in all simulated cases. This high pressure generated inflow from the sulcus and subsequent spiral internal flow, especially in fast ambient flows. This means that the sulcus generated the considerable pressure gradient around the gape passively and generated the stable intake of seawater and a spiral flow of water inside the shell for feeding. We conclude that the shell form of certain spiriferides could generate spiral flows so as to promote passive feeding, and the sulcus is interpreted as an important form for the passive intake of water.