The flexible manipulator is widely used in space robots, robot arm, and manufacturing industries that produce micro-scale products. This study aims to formulate the equation of motion of a flexible single-link manipulator system that moves translationally and rotationally and to develop computational codes with the finite-element method in performing dynamic simulation on the vibration of the flexible manipulator system. The system of the single-link flexible manipulator (SLFM) consists of an aluminium beam as a flexible link, a clamp part to hold the link, a DC motor to rotate the drive shaft, a trajectory to transfer the link in translational motion, and a servo motor to rotate the link. Computational codes in time history response (THR) and Fast Fourier Transform (FFT) processing were developed to identify the dynamic behaviour of the link. The finite-element method and Newmark-beta are used in simulating the SLFM. Simulation using the finite-element method has displayed dynamic behaviour through a graph of FFT on free vibration and THR graph on forced vibration by the excitation force due to the translational and rotational motions of the system. FFT has also generated natural frequency values as (f) 8.3 [Hz]. For translational and rotational motions, lateral deformation gets the maximum deviation at the value 0.0077 [m] and the minimum deviation -0.0085 [m] at t = 0 [s]. While at time t = 0.5 [s] due to the existence of the excitation force at the time, the maximum deviation at the value -0.009 [m], and the minimum deviation -0.0085 [m].