In recent days, study of topological Weyl semimetals have become an active branch of physics and materials science because they led to realization of the Weyl fermions and exhibited protected Fermi arc surface states. Therefore, topological Weyl semimetals Ta X ( X = P, As) are important electronic systems to investigate both from the point of view of fundamental physics and potential applications. In this work, we have studied the structural, elastic, mechanical, electronic, bonding, acoustic, thermal and optical properties of Ta X ( X = P, As) in detail via first-principles method using the density functional theory. A comprehensive study of elastic constants and moduli shows that both TaP and TaAs possesses low to medium level of elastic anisotropy (depending on the measure), reasonably good machinability, mixed bonding characteristics with ionic and covalent contributions, brittle nature and relatively high Vickers hardness with a low Debye temperature and melting temperature. The minimum thermal conductivities and anisotropies of Ta X ( X = P, As) are calculated. Bond population analysis supports the bonding nature as predicted by the elastic parameters. The bulk electronic band structure calculations reveal clear semi-metallic features with quasi-linear energy dispersions in certain sections of the Brillouin zone near the Fermi level. A pseudogap in the electronic energy density of states at the Fermi level separating the bonding and the antibonding states indicates significant electronic stability of tetragonal Ta X ( X = P, As).The reflectivity spectra show almost non-selective behavior over a wide range of photon energy encompassing visible to mid-ultraviolet regions. High reflectivity over wide spectral range makes Ta X suitable as reflecting coating. Ta X ( X = P, As) are very efficient absorber of ultraviolet radiation. Both the compounds are moderately optically anisotropic owing to the anisotropic nature of the electronic band structure. The refractive indices are very high in the infrared to visible range. All the energy dependent optical parameters show metallic features and are in complete accord with the underlying bulk electronic density of states calculations.