In this paper, we report about the effect of the application of a state of prestress on the band structure of a periodic phononic crystal characterized by an inertial amplification mechanism. Through a numerical example, we show the possibility of inducing negative group velocity in an isolated branch of the dispersion diagram. A 2-step Updated Lagrangian scheme is adopted to calculate the dispersion diagram of the structure. The proposed method include (i) the static geometrically nonlinear analysis of a representative unit cell undergoing the action of an applied external load and (ii) the BlochFloquet decomposition applied to the linearized equations of the acousto-elasticity for the unit cell in the deformed configuration. The dispersion analysis is performed in terms of small amplitude motions superimposed on a deformed state, once the desired load has been applied.