Development of nuclear fusion as a safe and virtually limitless power source receives growing attention in the context of looming energy crisis and climate change. ITER project stands as the flagship international project and advances steadily. Construction of the Tokamak Complex is nearly finished, and the assembly of core components has started in the site. In parallel, design is getting finalized and the safety case gets more concrete. Current approaches for radiation safety demonstration based in 3D nuclear analysis require sophisticated artifacts due to the consideration of separate MCNP models for the Tokamak and the rest of the facility, resulting in cumbersome studies and thus, debilitated conclusions. To improve this situation, we have built the first integral MCNP model of the ITER facility: the ITER full model. Accompanied by improvements to the D1SUNED code, we illustrate its computational practicality and pertinence in two meaningful simulations for ITER safety case. This work represents the culmination of a two-decades-long effort of ITER modelling seeking to demonstrate the radiation safety. Beyond supporting the remaining design tasks, this model represents a noticeable simplification in the approach to produce the corresponding 3D nuclear analysis. It improves the robustness of the first-of-a-kind ITER safety case.