The aim of this work is to compare several methods for the determination of very thin films Young's modulus and stress state: the nanoindentation test, the bulge test and the point-deflection method. The tested structures were silicon nitride and silicon nitride/silicon oxide bilayer membranes with different shapes (square or rectangular) and dimensions (from 1 mm to 3 mm). We report new experimental results on submicron thick dielectric membranes with thicknesses down to 100 nm. A Young's modulus of 217 ± 14 GPa have been found for silicon nitride membranes with a residual stress of 411 ± 30 MPa using the bulge test. Using nanoindentation experiments, a Young's modulus higher than 190 GPa has been estimated. The bulge test is still valid for the studied high dimension to thickness ratio membranes and more appropriate to determine the Young's modulus. A mixture law was shown to be possibly applied for Si3N4/SiO2 bilayer membranes for the Young's modulus and stress determination. The point deflection method is limited by the very low stiffness of these structures and only the residual stress can be accurately extracted. As the Young's modulus and membrane geometry have no significant influence on the stress determination by means of the point deflection method for the studied membranes (with a high lateral dimension to thickness ratio), more reliable results have been obtained such as 487 ± 40 MPa using an AFM cantilever for load-deflection experiments, for Si3N4 thin films.