The fundamental physics properties of the ternary bismuth tellurohalides (BiTeX (X=Br, I and Cl)) were investigated by using the ultra-soft pseudo-potential plane-wave (UPPW) within the general gradient approximation (GGA) in the frame of density functional theory (DFT). The calculated lattice constants are found in good agreement with the available experimental data. The calculated energy gaps are overestimated compared to the measured ones because the spin-orbit interaction (SOI) is not taken into account in this work. The elastic constants, shear modulus, Young׳s modulus, Poisson׳s ratioσ and the ratio B/G of BiTeX were calculated. According to the obtained results, the BiTeX are mechanically stable and the BiTeBr and BiTeI can be classified as brittle material, while the BiTeCl can be classified as ductile material. The shear anisotropic factors and the elastic anisotropy are also discussed. Finally, the Debye temperature and minimum thermal conductivity are obtained using theoretical elastic constants for the first time.