Aquatic flight, performed by rowing or flapping fins, wings or limbs, is a primary locomotor mechanism for many animals. We used a computer simulation to compare the mechanical performance of rowing and flapping appendages across a range of speeds. Flapping appendages proved to be more mechanically efficient than rowing appendages at all swimming speeds, suggesting that animals that frequently engage in locomotor behaviours that require energy conservation should employ a flapping stroke. The lower efficiency of rowing appendages across all speeds begs the question of why rowing occurs at all. One answer lies in the ability of rowing fins to generate more thrust than flapping fins during the power stroke. Large forces are necessary for manoeuvring behaviours such as accelerations, turning and braking, which suggests that rowing should be found in slow-swimming animals that frequently manoeuvre. The predictions of the model are supported by observed patterns of behavioural variation among rowing and flapping vertebrates.