The goal of this study is to investigate the mechanical and elastic characteristics of the Mn15Si26 compound via experimental nanoindentation measurements and ab-initio calculations. The mechanical properties such as Young’s modulus (E) and nanohardness are important inputs for improving the design and mechanical reliability of thermoelectric modules. The high-energy X-ray diffraction pattern of Mn15Si26 has been indexed with the Miller indices of a tetragonal crystalline structure whose cell parameters are the following: a = b = 5.535(3) Å and c = 65.552(4) Å. Nanoindentation measurements, with a Berkovich indenter tip have been performed on higher manganese silicide (HMS) compound mainly composed of Mn15Si26 grains. For the first time ever, it has been evidenced that both elastic modulus and nanohardness of the latter varied significantly depending on their crystallographic orientations provided by electron backscatter diffraction. Nanohardness and Young’s modulus along the< 001 > orientations are higher than the< 100 > ones. The nanohardness value of Mn15Si26 ranges from 16 GPa to 20 GPa and the Young’s modulus measured varies between 234 GPa and 300 GPa. The stiffness tensor (Sij = (Cij)−1) of Mn15Si26 has been deduced from these experimental measurements as well as calculated using Ab-initio calculations. The macroscopic elastic modulus (E, G, Β) and Poisson's coefficient have been examined and discussed and their 3D-representation has been plotted. The mechanical anisotropy hereby evidenced as the existence of anisotropy of the thermoelectric properties could be a significant factor for the mechanical reliability of thermoelectric modules which consisted of Mn15Si26 legs with a possible preferred crystallographic orientation induced during their fabrication.