In this work we theoretically study spectral multipole resonances of parallelepiped- and pyramid- silicon nanoparticles excited by linearly polarized light waves. We apply the numerical finite element method to calculate the scattering cross-sections as a function of the nanoparticles geometrical parameters. We use the multipole decom- position approach to explore optical resonances in silicon nanoparticles and the influence of second and third order multipoles to scattering diagrams. In contradistinction to our previous investigations, now we explore effects in near-IR spectral range. Apart from basic study we also obtained non-symmetrical combination of multipole contributions due to illumination from top and bottom sides of pyramids. Our work provides important information about the role of high-order multipoles in the light scattering by non-spherical and non-symmetrical nanoparticles. Our results can be applied, for example, for development of metasurfaces and metamaterials in near-IR spectral range.