Plesiosaurs are an enigmatic, diverse extinct group of Mesozoic marine reptiles well known for their unique body plan with two pairs of flippers and usually an elongated neck. The long neck evolved several times within the clade, yet the evolutionary advantages are not well understood. Previous studies have mainly focused on swimming speeds or flipper locomotion. We evaluated the hydrodynamics of neck length and thickness in plesiosaurs using computational fluid dynamics (CFD) simulations based on the Reynolds-averaged Navier-Stokes (RANS) approach. Simulations were performed of flow patterns forming around five distinctive plesiosaur models, three of different neck lengths (neck/body ratios of 0.2, 0.41, and 0.63) and two of different neck thicknesses (100% and 343% increase compared with cervical vertebrae width). By simulating water flow past the three-dimensional digital plesiosaur models, our results demonstrated that neck elongation does not noticeably affect the force of drag experienced by forward-swimming plesiosaurs. Thicker necks did reduce drag compared with thinner necks, however. The consistent drag coefficient experienced by the three neck lengths used in this study indicates that, at least for forward motion at speeds from 1 to 10 m/s, hydrodynamic implications were not a limiting selective pressure on the evolution of long necks in plesiosaurs. We also tested the effects of bending the long neck during forward motion. Bending a plesiosaur neck evenly in lateral flexion increased the surface area normal to flow and subsequently increased drag force. This effect was most noticeable in the longest-necked forms.