We study the correlation between the wake dynamics analyzed by numerical simulation and the general theory of aerodynamic instability of a flapping foil. The pure pitching motion and the pure heaving motion are considered in this paper. The main parameter is the Reynolds number, here we fixed the Reynolds number at Re = 1700. We found an interesting phenomenon in our research, which is that the lift amplitude CY of the numerical simulation is consistent with the the results of the general theory of aerodynamic instability, even at low frequencies where the additional mass effect is less important. And the average thrust CT(mean) increases exponentially with the Strouhal number SRA = fA/U, which is also an interesting phenomenon. By making the lift amplitude CY dimensionless with the amplitude θ0 and h 0, we find that the dimensionless lift amplitudes CY/θ0 or CY/h 0 are distributed along the same trend under different amplitudes. Through comparison and analysis of the pure pitching motion and the pure heaving motion, We clearly found that the lift on the heaving foil is slightly lower and the change of the lift is slightly more dramatic when the frequency is small.