Nanolaminated M(n+1)AX(n) phases as candidate materials for next generation nuclear reactor applications show great potential in tolerating radiation damage. However, different M(n+1)AX(n) materials behave very differently when exposed to energetic neutron and ion irradiations. Based on first-principle calculations, the radiation tolerance of two M(3)AX(2) and four M(2)AX phases were studied in this work, covering all the M(n+1)AX(n) phases previously investigated with experiments. We have calculated the formation energies of Frenkel pairs and antisite pairs in these materials. The improved radiation tolerance from Ti3AlC2 to Ti2AlC observed by experiments can be understood in terms of different Al/TiC layer ratio as the A atomic plane in the nanolaminated crystal M(n+1)AX(n) accommodates radiation-induced point defects. The formation of M-A-A(M) antisite pair in M(n+1)AX(n) materials would provide an alternative way to accommodate the defects resulted from radiation damage cascades, whereas this ideal substitution channel does not exist for Cr2GeC due to its pronouncedly higher M-A-A(M) antisite pair formation energy. To further elucidate their radiation damage tolerance mechanism, we have made a detailed analysis on their interatomic M-X, M-A, and X-A bonding characters. Criteria based on the bonding analysis are proposed to assess the radiation tolerance of the six M(n+1)AX(n) materials, which can be further applied to explore other M(n+1)AX(n) phases with respect to their performances under radiation environment.