Understanding how fish traverse man-made barriers (e.g. road-crossings and culverts) ensures that engineering and design guidelines achieve positive outcomes for fish communities. Water velocity, depth and fish body size are interrelated factors that influence fish passage through culverts. Velocity barriers have been a major focus of culvert remediation efforts to improve fish passage, however wide culvert designs that aim to limit high water velocities, often create shallow depths in the culvert barrel that can potentially impede fish passage. Here, we quantified how water velocity, depth and body size interact to affect fish swimming performance and their ability to traverse a 12 m culvert-scale swimming channel. Juveniles and sub-adults of three large-bodied native Australian fish species, silver perch (Bidyanus bidyanus), Murray cod (Maccullochella peelii) and eel-tail catfish (Tandanus tandanus), were chosen to represent a range of body shapes, swimming styles and capabilities. Each species was swum in nine treatments, consisting of three velocities at three water depths, with their time to fatigue and traverse success rates over 8 m of flume length quantified. We found that B. bidyanus had an exceptional probability of traverse success, with larger individuals traversing faster than smaller sized fish, but they were physically hindered by shallow water depths. The interaction between velocity and depth was non-linear and highly affected the swimming performance and traverse success of M. peelii and T. tandanus, particularly for fish >250 mm and < 100 mm. Our results demonstrate the importance of considering size class and species-specific swimming capabilities in culvert design criteria.