Axial vibrations and bit-bouncing phenomena in tunnel drilling systems can affect the pre-reinforcement process indispensable in really difficult geotechnical conditions. The aim of this paper is to analyze and control these vibrations arising along the drill pipes to develop an automatic drilling. We present a vibration model as a damped wave equation with Neumann boundary conditions. We use this model as well as the Resonant Sonic Head Drill (RSHD) one to define a reference trajectory. We propose a Flatness-based controller to tackle the position and velocity tracking problem ensuring an exponential convergence of the error dynamics and a desired drilling dynamical behavior. Simulation results confirm the efficiency of the proposed control law.