Abstract <p>The structural, elastic, mechanical, and electronic properties of chalcogenide perovskite BaHfS₃ with an orthorhombic-type structure under pressure were investigated using first-principles calculations. The calculated structural parameters and elastic constants show a good agreement with the experimental values. The details of pressure dependences of the structural parameters and elastic constants are also presented and discussed. Born’s structural stability criteria and phonon dispersion curves show that the structure of chalcogenide perovskite BaHfS₃ with the space group Pnma is mechanically stable up to 20 GPa. According to our calculation, the elastic constant <i>C</i>₁₁, <i>C</i>₂₂, <i>C</i>₃₃, <i>C</i>₁₂, <i>C</i>₁₃, and <i>C</i>₂₃ increase monotonically with the increasing pressure. However, the elastic constants <i>C</i>₄₄, <i>C</i>₅₅, and <i>C</i>₆₆ have little change with the increasing pressure. The&#xa0;<i>B</i>/<i>G</i> ratio and the Poisson’s ratio show that the orthorhombic BaHfS₃ behaves as a brittleness material at ambient pressure and has increment ductile under pressure. Meanwhile, the analysis of the electronic structures reveals that the states near the valence band top are derived from Hf 5<i>d</i> and S 3<i>p</i> orbitals and the lowest conduction band is composed of Ba 6<i>s</i>, Hf 5<i>d</i>, and S 3<i>p</i> orbitals. We expect that the findings predicted the physical properties of this compound will promote future experimental studies on chalcogenide perovskite BaHfS₃.</p>