To capture prey by suction, fish generate a flow of water that enters the mouth, and exits at the back of the head. It was previously hypothesized prey-capture performance is improved by a streamlined shape of the posterior region of the pharynx, which enables an unobstructed outflow with minimal hydrodynamic resistance. However, this hypothesis remained untested for several decades. Using computational fluid dynamics simulations, we now managed to quantify the effects of different shapes of the posterior pharynx on the dynamics of suction feeding, based on a feeding act of a sunfish (Lepomis gibbosus). In contrast to what was hypothesized, the effects of the imposed variation in shape were negligible: flow velocity patterns remained essentially identical, and the effects on feeding dynamics were negligibly small. This remarkable hydrodynamic insensitivity implies that, in course of the evolution, the observed wedge-like protrusions of the pectoral surfaces of the pharynx probably resulted from spatial constraints and/or mechanical demands on the musculoskeletal linkages, rather than constraints imposed by hydrodynamics. Our study therefore exceptionally shows that a streamlined biological shape subjected to fluid flows is not always the result of selection for hydrodynamic improvement.