Cross-flow turbine blades operate in an unsteady environment over large ranges of angle of attack and Reynolds number, often enduring dynamic stall. The hydrodynamics are further complicated because the circular orbit of the blades changes their effective curvature. In order to address these technical challenges with modeling cross -flow turbines, this article presents a novel dynamic stall model with flow curvature correction. The dynamic stall model extends Beddoes-Leishman dynamic stall theory, including several effects such as proper asymptotic behavior at large (similar to 90 degrees) angles of attack, influence of reduced -pitch rate on the stall angle, dynamics of the flow separation point, and changes in effective camber due to flow curvature. Further, the model enables rapid hydrodynamic analysis of cross -flow turbines using free vortex methods. Important design parameters such as blade thickness and camber are explicitly accounted for in the model, which enables parametric study of turbine configurations and therefore makes the model useful for system -level turbine optimization. Numerical predictions are validated by experimental data for several cases, including ranges of blade profile, toe angle, solidity, and tip speed ratio. (C) 2018 Published by Elsevier Ltd.