This paper describes and applies a methodology to determine the elastic properties of freestanding thin membranes by means of a bulge test and a numerical approach. The numerical procedure is based on the combination of two standard methods i.e. finite element analysis and classical analytical solutions to calculate elastic properties of thin films. Bulge tests were conducted on silicon nitride (Si3N4) monolayer of 2 x 2 mm (square) and 3.5 x 1.5mm (rectangular) membranes with the aim to determine elastics properties (Young's modulus (E) and Poison's ratio (v)) that define the load-deflection curves of both membranes. With this purpose, an error function was constructed for each membrane which involved finite element solutions, analytical solutions and experimental measurements. Error functions were found and minimized by mapping a set of elastic parameters for the two membranes (square and rectangular). A unique solution was determined in the intersection of both linear approximations, obtaining 236 GPa for E and 0.264 for v. It is well known that in a traditional bulge test analysis only one of both biaxial modulus can be determined and not a combination of E and v. Numerical results show that calculated load-deflection curves agree well with the measurements obtained for both square and rectangular membranes experimentally. The proposed methodology is only applicable in thin films with elastic behavior, however generalization for more complicated geometries is possible.