A systematic first-principle study is conducted to calculate bulk modulus, elastic constants, phonondispersion curves, and electronic structures of CeO 2 , ThO 2 , and their ordered binary alloys Ce x Th 8−x O 16 with x = 1, 2, 4, 6, and 7 using local-density approximation ͑LDA͒, generalized gradient approximation ͑GGA͒, LDA+ U, and GGA+ U approaches. In order to get accurate results for these type of systems including f electrons ͓Ce͑4f͒ and Th͑5f͔͒ we optimized the U parameter for use in LDA+ U and GGA+ U approaches. The computed structural, mechanical, and electronic properties of CeO 2 and ThO 2 are observed to display strong correlation with experimental data. In particular, the best agreement with experiment is obtained within the LDA+ U in which on-site Coulomb interaction parameter ͑U ef f ͒ for Ce and Th are taken as 6.0 and 5.0 eV. To check the stability of alloy forms, phonon-dispersion curves of Ce x Th 8−x O 16 with x = 2, 4, and 6 are computed. In all concentrations, mechanical stability conditions are satisfied for alloys. Furthermore, we observed no negative phonon branches in the phonon spectrum of alloys. Our calculations indicated a strong effect of concentration, x, on the electronic structure of Ce x Th 8−x O 16 .