In this paper, the stress influence in the guided wave velocity of the fundamentaltorsional mode is presented. Two analytical models, based on the Acoustoelasticity effect, tocompute the fundamental torsional mode velocity propagating in a specimen subject to anaxial stress are studied. These models are obtained due to the relation between the T(0, 1)guided wave velocity and the bulk shear velocity. The analytical models to calculate the guidedwave velocity are functions of the stress, second and third order elastic constants. A series ofaxial stress levels applied to a cylindrical waveguide is investigated with numerical simulations(Finite Elements) to estimate variations of the T(0, 1) guided wave velocity. This analysisprovides a criterion to evaluate the practical implementation of a stress monitoring schemebased on velocity variations of the fundamental torsional mode.