Failure of drill-strings is very costly in terms of money and time and occurs more frequently than oil companies would like to see. There are many reasons for drill-string failure, such as vibration, fatigue, and buckling. This paper addresses the problem of suppression of stick-slip oscillations in oil well drill-strings using proportional integral derivative (PID) and lead-lag controllers in conjunction with genetic algorithms. Simulation results are presented to validate the proposed control schemes.