The structural and elastic properties of polycrystalline tetragonal BaFCl have been calculated by ab initio firstprinciples calculations. The linear combination of atomic orbitals method within the density functional theory framework has been used. LDA, GGA (PBEsol), SOGGA and hybrid of HF and DFT, i.e. B3LYP schemes of CRYSTAL09 code were used for this study. Elastic constants, bulk modulus (B), shear modulus (G), Young’s modulus (E) and elastic anisotropies of BaFCl have been computed. The results showed that these compounds have large elastic isotropy incompressibility and small elastic anisotropy in shear. The computed data is in well agreement with earlier reported values.