Low cost “sailwing” aerofoils of flexible nylon mounted between a rigid leading edge of circular cross section and a rigid flat trailing edge were investigated in the 1970s and 1980s. Wind tunnel measurements of lift and drag of these aerofoils over the full range of angles of attack were published, but no predictions were made for a complete wind turbine incorporating them. Another paper stated that a sailwing turbine with aerofoils incorporating pivoting aerodynamic profile leading edges was found to exert considerable starting torque. In the present paper, published lift and drag data have been used to predict the performance of a small Darrieus hydrokinetic or wind turbine with sailwing aerofoils, using a standard multiple streamtube model over the full range of tip-speed ratios (TSRs) from 0.5 to 3. To provide a fair comparison, this method is also used to predict the performance of the turbine with symmetrical NACA0018 and cambered Gö420 blade profiles. At all examined TSRs, average torque and power of the turbine with flexible blades are higher than the turbines with rigid blades. For instance, at TSR of 2.5, the flexible blade turbine achieved 55 % and 165 % higher average torque than the turbines with symmetrical and cambered blades, respectively. This finding is attributed to the fact that the flexible blade camber reverses with reversing incidence, producing high lift coefficients at low incidence. Drag is higher for the flexible aerofoil, probably due to separation at the circular cross section leading edge, and measures are suggested to improve this. The flexible aerofoils are very cheap and simple to fabricate, making them an attractive option for affordable hydrokinetic turbines.