The structural, electronic, mechanic, vibrational and thermodynamic properties of Ti2SiB which is a hypothetical MAX phase compound, have been investigated using density functional theory calculations. The structural optimization of Ti2SiB has been performed and the results have been compared with Ti2SiC, Ti2SiN, and Ti2AlB that are studied in the literature. Then the band structure and corresponding partial density of states are computed. In addition, charge density and Bader charge analysis have been performed. The elastic constants have been obtained, then the secondary results such as bulk modulus, shear modulus, Young's modulus, Poisson's ratio, and Vickers Hardness of polycrystalline aggregates have been derived, and the relevant mechanical properties have been discussed. Moreover, the elastic anisotropy has been visualized in detail by plotting the directional dependence of compressibility, Poisson ratio, Young's and Shear moduli. Furthermore, the phonon dispersion curves as well as corresponding phonon PDOS, and thermodynamical properties such as free energy, entropy and heat capacity have been computed and the obtained results have been discussed in detail. This study provides the first considerations of Ti2SiB that could have a potential application in nuclear industry.