A theoretical studies of structural, electronic, elastic and high pressure properties in barium chalcogenides BaX (X = S, Se, Te, Po) are performed, using the full-potential augmented plane wave plus local orbitals method (FP-APW + lo). In this approach the local-density approximation (LDA) and generalized gradient approximation (GGA) are used for the exchange-correlation (XC) potential. Moreover, the alternative form of GGA proposed by Engel and Vosko (GGA-EV) is also used for band structure calculations. The equilibrium lattice constant and the bulk modulus agree well with the experiments. The pressures at which these compounds undergo structural phase transition from NaCl (B1) to CsCl (B2) phase were found to be in good agreement with the available experimental data. Results obtained for band structure using GGA-EV show a significant improvement over other theoretical work and are closer to the experimental data. A linear relationship is observed between theoretical band gap and 1/a 2 (where a is lattice constant).We have determined the elastic constants C 11 , C 12 and C 44 at ambient conditions in both B1 and B2 structures, which have not been established neither experimentally nor theoretically. Further, we have also calculated the pressure dependence of the elastic constants for the B1 structure of the four compounds.