This paper investigates possible effects of alpha particle and ion beam irradiation on the properties of the superinsulating phase, recently observed in titanium nitride films, by using numerical simulation of particle transport. Unique physical properties of the superinsulating state are considered by relying on a two-dimensional Josephson junction array as a model of material structure. It is suggested that radiation-induced change of the Josephson junction charging energy would not affect the current-voltage characteristics of the superinsulating film significantly. However, it is theorized that a relapse to an insulating state with thermally activated resistance is possible, due to radiation-induced disruption of the fine-tuned granular structure. The breaking of Cooper pairs caused by incident and displaced ions may also destroy the conditions for a superinsulating phase to exist. Finally, even the energy loss to phonons can influence the superinsulating state, by increasing the effective temperature of the phonon thermostat, thereby reestablishing means for an energy exchange that can support Cooper pair tunneling.