Various Mesozoic marine reptile lineages evolved streamlined bodies and efficient lift-based swimming, as seen in modern aquatic mammals. Ichthyosaurs had low-drag bodies, akin to modern dolphins, but plesiosaurs were strikingly different, with long hydrofoil-like limbs and greatly variable neck and trunk proportions. Using computational fluid dynamics, we explore the effect of this extreme morphological variation. We find that, independently of their body fineness ratio, plesiosaurs produced more drag than ichthyosaurs and modern cetaceans of equal mass due to their large limbs, but these differences were not significant when body size was accounted for. Additionally, necks longer than twice the trunk length can substantially increase the cost of forward swimming, but this effect was cancelled out by the evolution of big trunks. Moreover, fast rates in the evolution of neck proportions in the long-necked elasmosaurs suggest that large trunks might have released the hydrodynamic constraints on necks thus allowing their extreme enlargement.