Although the evaluation of theArtificial Neural Networks critical gallopingGalloping conditions is apparently very simple for one degree-of-freedom systems, whose expression is reported by many codes and guidelines, it hides pitfalls due to the uncertaintyUncertainty inherent in practically all the parameters involved, such as the static aerodynamic coefficientsAerodynamic coefficients and the structural damping ratio. Furthermore, if one intends to evaluate the possible nonlinear behavior of the dynamic system (e.g., for energy harvesting problems), the uncertaintiesUncertainty explode since high-order derivatives are needed to adequately describe the aerodynamic force coefficient. An Artificial Neural NetworkArtificial Neural Networks algorithm, suitably trained on simulated experimental data, appears to be a possible tool for providing more reliable evaluations of critical condition onset and nonlinear responses. The benchmark case of the square section with sharp and rounded corners is examined. Aerodynamic data are derived from the literature. Numerical simulation results concerning gallopingGalloping critical velocity are presented and compared against the theoretical solution.