The goal of this design process was to achieve the most efficient propulsive system for the candidate autonomous underwater vehicle (AUV) as possible. A mathematical approach, using fundamental motor equations and derived quantities, was used to characterize and select an efficient brushless electric motor for the propulsion system. A program developed at MIT, Massachusetts Institute of Technology, called OpenProp versions 1 and 2.3 was utilized to design a custom propeller that maximizes the efficiency of the system. A brushless electric motor was selected for the candidate AUV based on a survey of available off the shelf motors and a mathematical characterization process. In parallel with the motor characterization a propeller design was optimized using OpenProp v1 to perform a parametric analysis. OpenProp v2.3 was then used to design a unique propeller for the selected motor. The propeller design resulted in a final propeller with an efficiency of 79.93%. The motor characterization process resulted in two candidate motors being selected, the NeuMotor 1925-3Y and NeuMotor 1521-10.5Y, for in house testing and evaluation. A total propulsive system efficiency of between 44% and 46% was achieved depending on which motor is selected for the final design. / Master of Science