© 2019, © 2019 Atomic Energy Society of Japan. All rights reserved. To elucidate the mechanical properties of fuel debris inside the Fukushima Daiichi Nuclear Power Plant, we use first-principles calculations to evaluate mechanical properties of cubic ZrxU1−xO2, which is a main component of the fuel debris. We focus on the dependence of mechanical properties on the fraction x of zirconium and compare our results with recent experiment of simulated debris, in which dependences of elastic moduli and fracture toughness on the ZrO2 content showed deviation from a simple linear relation. We show that elastic moduli drop at around x = 0.25 and increase again for larger values of x, as has been observed in experiments. The reason of the drop is a softening owing to disordered atomistic structures induced by the solute zirconium atoms. We also find that stress–strain curves for the x = 0.125 case show marked hysteresis owing to the existence of many meta-stable states. We show that this hysteresis leads to slightly increased fracture toughness, but it is not enough to account for the significant increase of fracture toughness observed in experiments.