In this paper a numerical approach is developed to forecast the dynamic behavior of a power transmission belt running on eccentric pulleys. Basic partial differential equations are developed, considering the elastic effect of the lower branch of the belt. Nonlinear resonances and dynamic instabilities are analyzed in detail using a high dimensional discrete model, obtained through the Galerkin procedure. The numerical analysis is performed by means of direct simulations and a continuation software. Numerical results are compared with available experimental data. It is shown that the numerical method is able to predict correctly the amplitudes of oscillation in several operating conditions: direct and parametric resonances. Frequency response curves are obtained when the belt is harmonically excited close to the first and second linear natural frequency. The damping ratio and the linear frequencies are identified at zero axial speed.