Ternary M_(n+1)AX_n phases with layered hexagonal structures, as candidate materials used for next-generation nuclear reactors, have shown great potential in tolerating radiation damage due to their unique combination of ceramic and metallic properties. However, M_(n+1)AX_n materials behave differently in amorphization when exposed to energetic neutron and ion irradiations in experiment. We first analyze the irradiation tolerances of different M_(n+1)AX_n(MAX) phases in terms of electronic structure, including the density of states(DOS) and charge density map. Then a new method based on the Bader analysis with the first-principle calculation is used to estimate the stabilities of MAX phases under irradiation. Our calculations show that the substitution of Cr/V/Ta/Nb by Ti and Si/Ge/Ga by Al can increase the ionicities of the bonds,thus strengthening the radiation tolerance. It is also shown that there is no obvious difference in radiation tolerance between M_(n+1)AC_n and M_(n+1)AN_n due to the similar charge transfer values of C and N atoms. In addition, the improved radiation tolerance from Ti_3AlC_2 to Ti_2AlC (Ti_3AlC_2 and Ti_2AlC have the same chemical elements), can be understood in terms of the increased Al/TiC layer ratio. Criteria based on the quantified charge transfer can be further used to explore other M_(n+1)AX_n phases with respect to their radiation tolerance, playing a critical role in choosing appropriate MAX phases before they are subjected to irradiation in experimental test for future nuclear reactors. Ternary M_ (n + 1) AX_n phases with layered hexagonal structures, as candidate materials used for next-generation nuclear reactors, have shown great potential in tolerating radiation damage due to their unique combination of ceramic and metallic properties. However, M_ (n + 1) AX_n materials behave differently in amorphization when exposed to energetic neutron and ion irradiations in experiment. We first analyze the irradiation tolerances of different M_ (n + 1) AX_n (MAX) phases in terms of electronic structure, including the density of states DOS) and charge density map. Then a new method based on the Bader analysis with the first-principle calculation is used to estimate the stabilities of the MAX phases under irradiation. Our calculations show that the substitution of Cr / V / Ta / Nb by Ti It is also shown that there is no obvious difference in radiation tolerance between M_ (n + 1) AC_n and M_ (n + 1) AN_n d In addition, the improved radiation tolerance from Ti_3AlC_2 to Ti_2AlC (Ti_3AlC_2 and Ti_2AlC have the same chemical elements), can be understood in terms of the increased Al / TiC layer ratio. Criteria based on the quantified charge transfer can be further used to explore other M_ (n + 1) AX_n phases with respect to their radiation tolerance, playing a critical role in choosing an appropriate MAX phases before they are to irradi in experimental test for future nuclear reactors .