MAX phase carbides are a set of materials that have attracted the research and industrial interest due to their unique combination of metallic and ceramic properties. In recent experimental studies it was determined that Nb-based MAX phases have good mechanical and thermal properties. In the present systematic density functional theory study we examine the elastic behaviour and radiation tolerance of a range of Nb2AC (A = Al, Ga, Ge, In, Sn, As, P, and S) MAX phases. It is found that the Nb-based 211 MAX phases studied here are mechanically stable and elastically anisotropic. Elastically, Nb2GeC possesses the highest level of anisotropy and Nb2InC, the lowest. The cross-slip pinning process is enhanced in Nb2GeC that is considerably reduced in Nb2InC. Nb2GeC, Nb2SnC, and Nb2SC are ductile, whereas the other Nb-based MAX phases considered here are brittle in nature. In particular, Nb2GeC is highly ductile and Nb2AlC is more brittle. Nb2PC and Nb2SnC are respectively, more stiff and flexible under tension or compression. Nb2SnC has the best thermal shock resistance among the Nb-based MAX phase carbides studied here. Regarding the radiation tolerance of these MAX phases it is anticipated that Nb2SnC will be the most resistant to radiation.