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Two-body, Born–Mayer type potential considered up to the third nearest-neighbor interaction have been used to investigate the B1–B2 phase transition and elastic properties of barium chalcogenides at high pressure. The computed values of B1–B2 phase transition pressure, equation of state (compression curve), bulk modulus, and its first-order pressure derivative are given along with the available experimental and other theoretical values. This study supports the Born's stability criterion and shows that the third nearest-neighbor interaction has an important role to predict the B1–B2 phase transition pressure in barium chalcogenides.