The effect of pressure on the structural, elastic, and thermodynamic properties of SrTe in both B1 (rocksalt) and B2 (CsCl-type) phases and the SrTe1−xCax alloys with Ca dopant concentrations at x = 0.16667, 0.20, 0.33333, 0.42857, 0.44444 and 0.50 have been investigated using the two new gradient-corrected functional developed by Perdew, J.P.; Burke, K.; Ernzerhof named Density-Gradient Expansion for Exchange in Solids (PBEsol) and generalized Wu–Cohen (WC), in a significant range of pressure from 0 GPa to 30 GPa. The structure parameters, elastic stiffness constants cij, the bulk modulus (B), Kleinman parameter (\( \xi \)), shear anisotropies Ashear are also determined. Furthermore, as reported in this study, the aggregate elastic modulus (B, G, E), Poisson’s ratio (ν) and the Lame’s coefficients (λ) are estimated. On the other hand, the ductility, brittleness, longitudinal, transverse sound velocities and the Debye temperature ΘD(T) are also obtained. Importantly, our results are in reasonable agreement with the available theoretical and experimental data. To the best of our knowledge, this is the first study of the effect of the composition on the properties of the SrTe1−xCax alloys which may encourage other works for the confirmation of the reported results.