This thesis develops, implements and tests a mine search algorithm for the Naval Postgraduate School Autonomous Underwater Vehicle (Phoenix). The vehicle is 72 inches long and displaces 400 pounds. Its maneuvers are performed using two propellers and four thrustem. It contains two embedded computer systems. The algorithm directs the autonomous search of a specified area mapping all obstacles and computing an estimate of the cumulative probability of detection. The algorithm uses no prior knowledge of the terrain or the location of mines. The algorithm, which is written in Lisp, can execute on the vehicle's computer systems. Along with the search and mapping capabilities, the algorithm executes obstacle avoidance. The algorithm is tested in several simulated scenarios with different placement of mines and obstacles; the amount of resources used and the fraction of the area searched is computed. A similar algorithm that uses hill-climbing search is implemented for comparison. In all cases, the newly developed algorithm performed equal or better than the one that uses hill-climbing.