In this study, we investigate the effect of hydrofoil flexibility on the power extraction of a flapping tidal stream generator with hydrofoils down-scaled for a water channel in an experiment with a typical Strouhal number and frequency. The described deformations in the chord and spanwise directions are imposed onto the surfaces of the hydrofoil to analyze the flexibility effect. In a two-dimensional (2D) simulation, parameter studies of the chordwise flexure are conducted and a 30% improvement in the rate of the power-extraction efficiency is then achieved when the chordwise flexure is 20% of the chord length. In a three-dimensional (3D) simulation, the chordwise flexure of 20% achieves a 15% improvement in the rate of the power-extraction efficiency for the hydrofoil with an aspect ratio (AR) of 5, which is less than that in the 2D simulation due to 3D effects such as tip loss and a spanwise vortex. Meanwhile, the effect of the spanwise flexure on the power extraction is minor as compared to that of the chordwise flexure. It was also found throughout the parametric study of the AR variation that the 3D effect of the chordwise flexible hydrofoil is slightly stronger than that of the rigid hydrofoil.