CFD modelling of tidal turbines in arrays is described and assessed against experimental studies of turbines operating either at constant speed or constant torque. Rotor blades are represented by rotating actuator lines, whilst supports are represented by partially-blocked-out cells. For a single turbine the model successfully reproduces towing-tank measurements of thrust and power coefficients across a range of tip-speed ratios. For two turbines staggered streamwise, it is demonstrated that loads may be reduced or augmented, according as the downstream turbine is in the wake or bypass flow of the upstream turbine. When the downstream turbine is partially in the wake, individual blades are subject to large cyclic load fluctuations. Array performance is evaluated by comparison with experimental data, modelling up to 12 turbines in up to three staggered rows. The speed of each turbine is continuously adjusted in response to flow-induced torque. Distribution of thrust coefficients within the array is well reproduced, but there is greater discrepancy in angular speed. With actuator representation of blades, the choice of turbulence model has little effect on load coefficients for an isolated turbine or row of turbines, but a significant effect on the wake, and hence on downstream turbines in an array.