Pressure- and temperature-dependent mechanical, elastic, and thermodynamical properties of rock salt to CsCl structures in semiconducting SrX (X=O, S, Se, and Te) chalcogenides are presented based on model interatomic interaction potential with emphasis on charge transfer interactions, covalency effect, and zero point energy effects apart from long-range Coulomb, short-range overlap repulsion extended and van der Waals interactions. The developed potential with non-central forces validates the Cauchy discrepancy among elastic constants. The volume collapse (VP/V0) in terms of compressions in SrX at higher pressure indicates the mechanical stiffening of lattice. The expansion of SrX lattice is inferred from steep increase in VT/V0 and is attributed to thermal softening of SrX lattice. We also present the results for the temperature dependent behaviors of hardness, heat capacity, and thermal expansion coefficient. From the Pugh’s ratio (f=BT/GH), the Poisson’s ratio (n) and the Cauchy’s pressure (C12–C44), we classify SrO as ductile but SrS, SrSe, and SrTe are brittle material. To our knowledge these are the first quantitative theoretical prediction of the pressure and temperature dependence of mechanical stiffening, thermally softening, and brittle nature of SrX (X=O, S, Se, and Te) and still await experimental confirmations.