Elastic properties of the solid-state CdTe1−xSex (x = 0 − 0.5, with ∆x = 0.125) solutions within the framework of density functional theory calculations were investigated. The structures of the CdTe1−xSex samples are obtained by the substitution of tellurium with selenium atoms in cubic CdTe. Young's modulus, shear modulus, bulk modulus, and the Poisson ratio of CdTe1−xSex crystals were calculated from the rst principles. The dependences of the elastic properties of the CdTe1−xSex solid solution on the content index x within the interval 0 ≤ x ≤ 0.5 are analyzed. According to the Frantsevich rule and the value of the Poisson ratio, the materials have been classied as ductile. The Zener anisotropy factor and the Kleimann parameter are calculated on the basis of the elastic constants Cij . Also, the concentration dependence of longitudinal elastic wave velocity, transverse elastic wave velocity, and average sound velocity, are calculated. Based on the average sound velocity the concentration behavior of the Debye temperature was calculated. The correlation analysis shows a good agreement between the calculation results (elastic modulus and Debye temperature) and known experimental data.