Efficiency in drilling is measured by Mechanical Specific Energy (MSE). MSE is the measure of the amount of energy input required to remove a unit volume of rock, expressed in units of energy input divided by volume removed. It can be expressed mathematically in terms of controllable parameters; Weight on Bit, Torque, Rate of Penetration, and RPM. It is well documented that minimizing MSE by optimizing controllable factors results in maximum Rate of Penetration. Current methods for computing MSE make it possible to minimize MSE in the field only through a trial-and-error process. This work makes it possible to compute the optimum drilling parameters that result in minimum MSE. The parameters that have been traditionally used to compute MSE are interdependent. Mathematical relationships between the parameters were established, and the conventional MSE equation was rewritten in terms of a single parameter, Weight on Bit, establishing a form that can be minimized mathematically. Once the optimum Weight on Bit was determined, the interdependent relationship that Weight on Bit has with Torque and Penetration per Revolution was used to determine optimum values for those parameters for a given drilling situation. A project of this size and duration is only possible with a great deal of support. My wife, Debbie, has been my greatest benefactor, and I could not have done it without her unwavering devotion. I would also like to thank my kids, Scott and Caroline, for their patience and inspiration. My parents, Louis and Barbara Hamrick are the most generous people I have ever encountered, and I could never have even begun the project without their backing. My father, through his company Northco, was particularly generous with lending machine time and funding for experimentation at the end of the project when all other sources were exhausted. I would like to thank URS Corporation and National Energy Technology Laboratory for providing infrastructure and financial support. Technical and moral assistance was lent by many people, including each member of my committee. Each of them deserves a measure of appreciation for their individual and collective service. Of particular assistance outside of my committee were Peter Zhang, who was always available for help sample preparation, and Jared Tannenbaum, who helped with load cells and micro-cracking. v