Autonomous Underwater Vehicles (AUVs) provide a useful means of collecting detailed oceano-graphic information. The hull resistance of an AUV is an important factor in determining the power requirements and range of the vehicle. This paper describes a procedure using Computational Fluid Dynamics (CFD) for determining the hull resistance of an AUV under development, for a given propeller rotation speed and within a given range of AUV velocities. The CFD analysis results reveal the distribution of the hydrodynamic values (velocity, pressure, etc.) around the AUV hull and its ducted propeller. The paper then proceeds to present a methodology for optimizing the AUV profile in order to reduce the total resistance. This paper demonstrates that shape optimization of conceptual designs is possible using the commercial CFD package contained in Ansys$^{TM}$. The optimum design to minimize the drag force of the AUV was identified for a given object function and a set of constrained design parameters.