Among various degradation mechanisms possibly affecting the long-term operation of nuclear power plants, the effects of induced expansion and internal degradation occurring in concrete exposed to high-flux neutron radiation require additional research. Notably, using short-term test-reactor data to assess the long-term structural significance of light-water reactor concrete biological shields necessitates properly capturing the concurrent time-dependent effects, e.g., creep and damage caused by radiation-induced volumetric degradation. As this poses significant numerical challenges, a creep-damage algorithm was developed to account simultaneously for the progress of damage and viscoelastic processes in the concrete microstructure. The algorithm uses a time-adaptive scheme in which the instants at which damage occurs are explicitly searched for. This provides a nonlocal continuum damage procedure with very low sensitivity to the time or loading step. The proposed method is then used to simulate creep and restraint effects on radiation-induced degradation in concrete.