This paper is devoted to the theoretical study of the extinction spectra of copper monosulfide particles under conditions of localized surface plasmon resonance. The study was conducted for plasmonic copper monosulfide particles of spherical and ellipsoidal shapes of variable size in media with different values of the refractive index. The simulation results reveal that increasing the radius of CuS nanoparticles leads to a significant enhancement in the amplitude of the plasmon peak and a shift of the peak towards longer wavelengths. It was investigated how the positions of the extinction peaks on the spectral scale and their amplitudes change when the particles deviate from the spherical shape. Simulations were performed for spherical and elongated ellipsoidal particles with fixed cross-sectional radius and variable length. Specifically, we varied the length of the major axis while keeping the lengths of the minor axes constant. It is shown that the deviation from the sphericity of the particles will affect both the position of the extinction maximum on the spectral scale and the shape of the spectral curve. An increase in the ratio of the ellipsoid semi-axes lengths leads to a significant increase in the amplitude of the extinction peak and its shift to the long-wavelength region. Besides, the position of the plasmonic peak on the spectral scale is influenced not only by the geometric parameters of the particles such as size and shape but also by the dielectric properties of the surrounding medium, including its refractive index. We assess the impact of changing the refractive index of the surrounding medium on the shape, amplitude, and position of the extinction maxima of CuS nanoparticles. It is showed that increasing the refractive index of the surrounding medium leads to a significant shift of the plasmon resonance peak into the long-wavelength region of the spectrum an increase in the peak width, and a decrease in its amplitude. Thus, ellipsoid copper monosulfide particles show improved surface plasmon characteristics compared to spherical ones and can be effectively used in the near-infrared spectral region.