The effect of nanostructuring on the mechanical and thermal properties of [SiO2/Si3N4](n) multilayer membranes, where n is the number of repetitions, was studied. It also was theoretically found that, when the membrane thickness is decreased, the mechanical deformation of the layers at a given pressure must take into account the transition from linear to nonlinear stress mechanism. This corresponds to the experimental results of testing the strength of round SiO2 (600 nm)/Si3N4 (130 nm)/SiO2 (400 nm)/Si3N4 (130 nm) multilayer membranes of different diameters of 1 mm, 1.4 mm, 1.8 mm respectively, within the measurement error. The good agreement between the numerical and analytical calculation of the equivalent heat capacity, thermal conductivity, and density of [SiO2/Si3N4](n) multilayer membrane of different thickness and composition (for n = 8, 16, 28) is demonstrated. A decrease in the equivalent thermal conductivity of [SiO2/Si3N4](n) membrane with increasing n is shown, which corresponds to the predominant heat propagation along the boundary of the layers. The results obtained can be used in the development of nanostructured [SiO2/Si3N4](n) multilayer membranes for various applications, such as Micro-Electro-Mechanical Systems (MEMS), bio-, gas-, pressure-sensors, X-ray sources and ultra-strong thin coatings.