Namnabat et al. (cf., [Carbon Letters, https://doi.org/10.1007/s42823-020-00194-2]) employ the classical approach of Li and Chou (cf., [Int J Solids Struct 40: 2487–2499]) to the implementation of the molecular structural mechanics method using the Bernoulli–Euler beam elements for nonlinear buckling analysis of double-layered graphene nanoribbons. However, more recent studies by Eberhardt and Wallmersperger (cf., [Carbon 95: 166–180]) and others (see, e.g., [Int J Eng Sci 133: 109–131]) have shown that the classical approach of Li and Chou poorly reproduces both in-plane and out-of-plane mechanical moduli of graphene. We have shown that the 2D beam-based hexagonal material used by Namnabat et al. poorly simulates the mechanical moduli of graphene, especially the bending rigidity modulus, and this material cannot be used for the buckling simulation of graphene sheets (or nanoribbons). In addition, it is noted that in Int J Eng Sci 133: 109–131, a modification of the classical approach of Li and Chou is given which exactly reproduces both in-plane (2D Young’s modulus and Poisson’s ratio) and out-of-plane (bending rigidity modulus) mechanical moduli of graphene using beam elements.