Silicon nitride (Si3N4), due to its high dielectric constant and low leakage current, is a perspective material for the fabrication of dielectric nanolayers in nanocapacitors. It is proposed to use Si3N4 in nanocapacitors operating in harsh conditions, such as under action of ionizing radiation. To eliminate the pinhole defects that facilitate dielectric breakdowns in nonthin layers, Si3N4 was fabricated as a stack of several Si3N4 nanolayers where each subsequent nanolayer covered the pinholes of the previous one. In this study, we compared radiation stability of 40 and 60 nm thick multi-layered Si3N4 nanofilms which were deposited on SiO2 and polySi substrates. The nanofilms were irradiated with 1 kGy of 5 MeV Bremsstrahlung rays using a linear electron accelerator ELU-4 (Salaspils, Latvia) and the effect of irradiation on chemical bonds of Si3N4 was analysed using a Bruker Vertex 70v Fourier transform infrared (FTIR) spectrometer. According to FTIR, the main chemical bonds remained unchanged after irradiation. Variations in the intensity of signals were attributed to the inhomogeneity of the deposited Si3N4 layers and not to the influence of radiation. The results show that Si3N4 multilayers are stable after exposure up to 1 kGy dose of Bremsstrahlung rays and can be used in nanocapacitors exploited in harsh radiation conditions.