We report the mechanical strength of native cellulose nanofibrils. Native cellulose nanofibrils, purified from wood and sea tunicate, were fully dispersed in water via a topochemical modification of cellulose nanofibrils using 2,2,6,6-tetramethylpiperidinyl-1-oxyl (TEMPO) as a catalyst. The strength of individual nanofibrils was estimated based on a model for the sonication-induced fragmentation of filamentous nanostructures. The resulting strength parameters were then analyzed based on fracture statistics. The mean strength of the wood cellulose nanofibrils ranged from 1.6 to 3 GPa, depending on the method used to measure the nanofibril width. The highly crystalline, thick tunicate cellulose nanofibrils exhibited higher mean strength of 3-6 GPa. The strength values estimated for the cellulose nanofibrils in the present study are comparable with those of commercially available multiwalled carbon nanotubes.