We have investigated the structural, elastic, electronic, optical and thermal properties of CsBaF3 perovskite using the full-potential linearized augmented plane wave method within the generalized gradient approximation and the local density approximation. Moreover, the modied BeckeJohnson potential (TB-mBJ) was also applied to improve the electronic band structure calculations. The ground state properties such as lattice parameter, bulk modulus and its pressure derivative were calculated and the results are compared with the available theoretical data. The elastic properties such as elastic constants, anisotropy factor, shear modulus, Young's modulus and Poisson's ratio are obtained for the rst time. Electronic and bonding properties are discussed from the calculations of band structure, density of states and electron charge density. The contribution of the dierent bands was analyzed from the total and partial density of states curves. The dierent interband transitions have been determined from the imaginary part of the dielectric function. The thermal eect on the volume, bulk modulus, heat capacities CV and the Debye temperature was predicted using the quasi-harmonic Debye model, in which the lattice vibrations are taken into account.