This study was designed to investigate the mechanical properties of the coating layer on electronic galvanized sheet steel as a part of the ongoing research on the coated steel. Those properties were determined using nano-indentation, the finite element method, and artificial neural networks. First and foremost, the load-displacement curve (the loading-unloading curve) of coatings was derived from a nano-indentation test by CSM (continuous stiffness measurement) and was used to measure the elastic modulus and hardness of the coating layer. The properties derived were applied in FE simulations of a nano-indentation test, and the analytical results were compared with the experimental result. A numerical model for FE simulations was established for the coating layer and the substrate separately. Finally, to determine the mechanical properties of the coating, such as the stress-strain curve, functional equations of loading and unloading curves were introduced and computed using the neural networks method. The results show errors within $5\%$ in comparison with the load-displacement measured by a nano-indentation test.