This book describes the design of a drilling chamber for the Resonance Enhanced Drilling (RED) technology invented by Professor Marian Wierecigroch at the University of Aberdeen. Most oil and gas wells are drilled using rotational drilling and a few with percussive drilling. Some technological advances have allowed some to combine both methods. RED is a smart way of combining both rotational and oscillatory motion to aid the drilling process and increase the rate of penetration. Analytical analysis of the stresses which the chamber would be subjected to were calculated and a numerical analysis was carried out to validate the results gotten in the analytical analyses. Finally, conclusions and recommendations for further work are suggested.