Uranium has been identified as an element of interest for the safety assessment of a deep geological repository for used nuclear fuel. This paper examines the sorption behavior of U(VI) onto MX-80 bentonite and granite in Ca-Na-Cl solutions of varying ionic strengths [0.05 to 3 mol/kgw (m)] and across a pH range of 4 to 10. U(VI) sorption on MX-80 showed that U(VI) sorption gradually increased with pHm until pHm = 6, where it reached its maximum, and decreased slightly with pHm until pHm = 8, and then became constant. U(VI) sorption on granite increased along with pHm, reached the maximum around pHm = 7 to 8, and then slightly decreased with pHm. Both MX-80 and granite showed essentially no ionic strength dependence for sorption of U(VI). A nonelectrostatic surface complexation model successfully predicted sorption of U(VI) onto MX-80 and granite using the formation of an inner-sphere surface complex. Optimized values of surface complexation reaction constants (log K0) for the formation reactions of these surface species are proposed.