Natural flight has always been the source of imagination for Mankind, but reproducing the propulsive systems used by animals that can improve the versatility and response at low Reynolds number is indeed quite complex. The main objective of the present work is the computational study of the influence of the Reynolds number, frequency, and amplitude of the oscillatory movement of a NACA0012 airfoil in the aerodynamic performance. The thrust and power coefficients are obtained which together are used to calculate the propulsive efficiency. The simulations were performed using ANSYS Fluent with a RANS approach for Reynolds numbers between 8500 and 34,000, reduced frequencies between 1 and 5, and Strouhal numbers from 0.1 to 0.4. The aerodynamic parameters were thoroughly explored as well as their interaction, concluding that when the Reynolds number is increased, the optimal propulsive efficiency occurs for higher nondimensional amplitudes and lower reduced frequencies, agreeing in some ways with the phenomena observed in the animal kingdom.