The discrete sources method is used to study the influence of quantum effects arising in the gold and silver cores of layered nanoparticles with a dense dielectric coating. This coating is designed to prevent particle clustering without reducing the energy absorbed by the particle. The study found that the absorption cross section of layered particles with a silver core is four times larger than that of particles with a gold core. It was also determined that the dielectric coating does not reduce the absorbed energy compared to homogeneous metal nanoparticles. It was shown that varying the elongation of the core allows the absorption cross section maximum to be shifted toward the transparency region of biological tissue, while varying the equivolume diameter of the core has virtually no effect on the position of the absorption cross section maximum in the wavelength range. The influence of quantum effects is limited to a shift of the absorption cross section maximum toward shorter wavelengths by 15 nm and a slight decrease in its magnitude. Keywords: layered nanoparticles, gold and silver cores, quantum effects, mesoscopic boundary conditions, Feibelman parameters, discrete sources method.