The development of a blade element momentum (BEM) model for the hydrodynamic design of marine current turbines is presented. The model includes routines for interpolation of 2D section data and extrapolation for stall delay. The numerical model is compared with experimental data obtained from tests of an 800 mm diameter model rotor carried out in a cavitation tunnel. The theoretical predictions are in good agreement with the experiments. Using this validated model, a typical 3D rotor is used to demonstrate parametric variations of the design parameters. The effect of tip immersion on possible cavitation is assessed for this rotor. The model is then used to solve the dynamic effects of a tidal profile. The effect of an increase in blade roughness is presented, indicating a relatively small reduction in power. This work demonstrates that the numerical model developed can provide a useful tool for the investigation of the hydrodynamic design and operation of marine current turbines.