The energy band structure, energy band gaps, refractive index, high-frequency dielectric constant, static dielectric constant, reflectivity, and susceptibility for CdTe and ZnTe have been determined. The elastic parameters, Young’s, bulk, shear moduli, Poisson ratio, anisotropic factor, and the internal strain parameter have been calculated for the CdTe and ZnTe. The acoustic velocity in the directions [001], [110], and [111] has been determined for the studied compounds. The pressure dependence of the investigated properties has been studied. The empirical pseudopotential method (EPM) was used to calculate our results. Our results at high values of pressure could be taken as a reference for future experimental and theoretical works. Generally, our results are found to be in good accord with experimental and theoretical data published in the literature. The data gained in this study could be useful in the development of optoelectronic devices under high values of pressure.