The measurements obtained with the falling weight deflectometer are typically used in a linear-static backcalculation procedure to determine the mechanical parameters of the asphalt pavement. The surface deflections caused by the FWD is a dynamic problem usually treated as a static problem. A dynamic solution of the backcalculation problem is proposed using a viscoelastic model, introducing a viscosity variable. The accuracy of the results is calculated taking the maximum deflection of every curve. The viscosity parameter allows simulate the whole deflection curve including its maximum value, the time interval between starting and finish of the deflection process, and the time delay between curves associated with geophones. The parameters of the model have been calibrated from experimental tests to create a database for different asphalt pavement sections. The backcalculation procedure is completed using an artificial neural network (ANN) to predict mechanical properties from a multilayered pavement for different configurations of the ANN.