The electronic band structure and elastic properties of the Cd${}_{16}$Se${}_{15}$Te solid state solution in the framework of the density functional theory calculations are investigated. The structure of the sample is constructed on the original binary compound CdSe, which crystallizes in the cubic phase. Based on the electronic band structure, the effective mass of electron, heavy hole, light hole, spin-orbit effective masses and reduced mass in G point are calculated. In addition, the exciton binding energy, refractive index and high-frequency dielectric constant are calculated. The Young modulus, shear modulus, bulk modulus and Poisson ratio are calculated theoretically. Based on the results of elastic coefficients, the value of acoustic velocity and Debye temperature is obtained.