The effect of a weak nonbonded layers interaction on the bending resistance of a multilayered graphene nanoribbon is studied. A numerical simulation of bending of a finite multilayered nanoribbon and analysis of its bending vibrations show that interaction of layers significantly increases bending stiffness normalized to a number of layers only for nanoribbons with length L > 12 nm. The greater the length, the stronger this increase. Thus, at length L = 24 nm, layers interaction increases bending stiffness three times for a two-layer nanoribbon and six times for a nine-layer nanoribbon. Therefore, the use of multilayered nanoribbons can significantly increase the bending resistance of extended nanoconstructions.