This research describes the dynamic modeling and numerical simulation of an autonomous underwater vehicle (AUV) with five hydrodynamic control surfaces, necessary for the development of an autopilot algorithm, based solely upon analytical methodologies. The purpose of this research was to demonstrate the ability to develop a low order approximation of the dynamics and control characteristics of an underwater vehicle that is complete enough to validate a specific design before physical construction begins; therefore, allowing for a more cost effective virtual design, test, and evaluation process. The AUV model developed in this study takes into consideration inertia, hydrostatic forces, hydrodynamic forces, propulsion forces, control fin forces, added mass, and damping. The model assumes that the vehicle is sufficiently far enough away from the bottom and the surface so that their effects can be ignored. The necessary stability and control derivatives were determined through the use of engineering formulae. The mathematical model represents a general, nonlinear, six degrees of freedom model, and it is similar to those used to carry out atmospheric flight simulations. The non-linear model was linearized about the design (equilibrium) condition to obtain a linear state-space vehicle model.