This paper presents quantum chemistry study on structural and mechanical properties of a series of single-walled carbon nanotubes (SWCNTs) and boron nitride nanotubes (BNNTs) functionalized with carbenes. At the PBE/SVP level, the obtained data on pristine nanotubes are in good accordance with the results of previous experimental and theoretical studies. The calculations show that carbenes functionalization, in general, distorts both SWNCTs and BNNTs frameworks, but there exists the difference between 'axial' and 'circumferential' functionalization. It turns out that in both cases elastic properties diminish with increasing concentration of adsorbents, however, the functionalized SWCNTs and BNNTs remain strong enough to be suitable for reinforcement of composites.