The purposes of this research are to derive the equations of motion of a flexible single-link system by a finite-element method, to develop the computational codes in order to perform dynamics simulations with vibration control and to propose an effective control scheme of a flexible single-link manipulator using two control strategies, namely proportional-derivative (PD) and active-force (AF) controls. The flexible manipulator used in this paper consists of an aluminum beam as a flexible link, a clamp-part, a servo motor to rotate the link and a piezoelectric actuator to control vibration. Computational codes on time history responses, FFT (Fast Fourier Transform) processing and eigenvalues - eigenvectors analysis were developed to calculate the dynamic behavior of the link. Furthermore, the PD and AF controls strategies were designed and compared their performances through the calculations. The calculated results show the superiority of the proposed AF control comparing the PD one to suppress the vibration of the flexible single-link manipulator.