A new atomistic structural model is developed here for graphene sheets based on thestiffnesses from the REBO potential. Using this model, the flexural vibration naturalfrequencies and buckling loads of rectangular single-layer graphene sheets of different sizes,chiralities and boundary conditions are calculated. The newly developed atomisticstructural model is verified by comparing the calculated fundamental natural frequenciesfor small-sized graphene sheets with those obtained from ab initio density functional theory(DFT) frequency analysis. The vibration and buckling analysis results are also comparedwith those of an earlier atomistic structural model based on the AMBER potential as wellas the equivalent continuum model for graphene sheets. Through this study, it isobserved that graphene sheets display very slight anisotropic characteristics inflexural vibration and buckling. Also, it is shown that the atomistic structuralmodel cannot be replaced by a classical equivalent continuum model such asa plate model. Most significantly, we verify that the new atomistic structuralmodel based on the REBO potential predicts more accurate natural frequenciesand buckling loads for graphene sheets, which are considerably lower than thosepredicted by the earlier atomistic structural model based on the AMBER potential.