The present work shows a load-deflection bulge test method to characterize mechanical parameters of thin films by means of a numerical modelling approach. A methodology based on the combination of finite element analysis and classical analytical equations is presented and discussed. Finite element modeling was conducted for monolayer (Si3N4) and bi-layer (Si3N4/Al) membranes with the aim to determine a set of elastic parameters (Young's modulus and Poisson's ratio) which satisfied the load-deflection curves experimentally measured by the bulge test method. It is well known that in a traditional bulge test analysis only biaxial elastic modulus, i.e. a combination of Young's modulus and Poisson's ratio, can be determined. It is due to the mechanical coupling that exists between the two elastic parameters. However, in this study both mentioned elastic constants can be determined independently through a proposed numerical procedure that includes error functions for minimizing the displacement with a specific set of optimal elastic parameters. Results shows that the estimated Young's modulus (Al 64 GPa and Si3N4 236 GPa) agree with corresponding values determined by other methods in the literature of the studied thin films.