A study has been made of the mechanical strength of a membrane element. The element is a two-layer structure of silicon oxide and silicon nitride on a silicon substrate. The critical pressure of a circular membrane is experimentally determined for various diameters. The elastic deformation has been shown as well as the distribution of mechanical stresses along the membrane diameter by numerical simulation in the COMSOL program. The area of critical deformation of membrane has been indicated. A comparison of the results of analytical calculation, numerical simulation and experiment has been made.