This work presents a mathematical study to obtain the coefficients that define the dynamics of an autonomous underwater vehicle (AUV), the Guanay II vehicle, with 3 degrees of freedom. This dynamics is given by several forces and moments (hydrostatic, hydrodynamic, added masses and propellers), which largely depend on the vehicle geometry. The Guanay II AUV has been designed following a Myring profile,which improves the hydrodynamics of the vehicle but also yields a tractable mathematical model. The model describes the geometric characteristics of the vehicle and the disposition of the thrusters and has backward movement capacity. The model has been tested by means of simulations and a prototype has been validated in real navigation.