In this work, the full-potential linearized augmented plane wave (FP-LAPW) method was used to calculate the structural, electronic, thermal and thermodynamic properties of BaS and CaS compounds and their ternary mixtures, Ba1−xCaxS. The local-density approximation (LDA), the Wu-Cohen generalized gradient approximation (WC-GGA) and the Perdew-Burke-Ernzerhof generalized gradient approximation (PBE-GGA) were used as the exchange-correlation potential. Moreover, the modified Becke–Johnson approximation was also used for the band structure calculations. We examined the composition effect on the lattice constants, bulk modulus and band gap. The microscopic origins of the band gap bowing were characterized in detail using the approach of Zunger and colleagues. Pressure and temperature effects on the lattice parameter, heat capacity, Debye temperature, Grüneisen parameter, and thermal expansion coefficient were predicted using the quasi-harmonic Debye model. The thermodynamic stability of these alloys was investigated by calculating the excess enthalpy of mixing, ∆Hm, and the phase diagram. It was shown that these alloys are stable at high temperature.