The relaxation of free electron–hole pairs generated after proton irradiation is modelled by means of a simplified set of hydrodynamic equations. The model describes the coupled evolution of the electron–hole pair and self-trapped exciton (STE) densities, along with the electronic and lattice temperatures. The equilibration of the electronic and lattice excitations is based on the two-temperature model, while two mechanisms for the relaxation of free electron–hole pairs are considered: STE formation and Auger recombination. Coulomb screening and band gap renormalisation are also taken into account. Our numerical results show an ultrafast ($${\ll }\,{\mathrm {1}}$$ ≪ 1 ps) free electron–hole pair relaxation time in amorphous $${{\mathrm {SiO}}_{\mathrm {2}}}$$ SiO 2 for initial carrier densities either below or above the exciton Mott transition. Coulomb screening alone is not found to yield the long relaxation time ($${\mathrm {\gg }}{\mathrm {10}}$$ ≫ 10 ps) experimentally observed in amorphous $${{\mathrm {SiO}}_{\mathrm {2}}}$$ SiO 2 and borosilicate crown glass BK7 irradiated with high-intensity laser pulses or BK7 irradiated by short proton pulses. Another mechanism, e.g. thermal detrapping of STEs, is required to correctly model the long free electron–hole pair relaxation time observed experimentally. Graphical Abstract