Graphene has captured significant scientific interest and funding due to its exceptional chemical and physical properties [1, 2, 3]. Understanding graphene’s mechanical behavior is crucial for optimizing its applications, necessitating accurate computational models. It therefore follows not only that constitutive models play a pivotal role in mechanical characterization, but also that the choice of the physical scale must be carefully selected. Specifically, our focus will center on the nano-scale, which we consider the appropriate physical scale for investigating significant phenomena such as hole laceration, defects propagation, high deformation gradients, and for calibrating interatomic potentials conducive to comparisons with Solid State Physics [4]. In this perspective, starting from the particle-based model of Molecular Statics [5], we aim to develop both accurate and efficient numerical tools, by proposing a multilevel approach able to overcome well-known limitations of two contrasting approaches, namely particle-based and continuum-based methods [6]. The former shows inefficiency due to their inherent extra computing time and costs; the latter suffers from inaccuracy especially in presence of localizations caused by nonlinear interatomic response. The proposed multilevel approach is an iterative solution strategy that can be regarded as a root-node based algebraic multigrid method [7] working with two nested scale-levels of corrections: a global level based on coarse mesh of Finite Elements collecting a certain patterns of atoms, a local level based on an interatomic correction at the nano-scale. The Finite Element is characterized through a numerical identification of the local pattern of the atoms, and is addressed to cheaply solve long-wavelength distribution of the whole solution [8]. Numerical results will be presented in both linear and nonlinear contexts, specifically referred to the in-plane mechanical response of single-layer graphene sheets. The numerical investigation will focus on the convergence and performance properties of the proposed strategy, also offering a discussion on the spectral response of the coarse level, and on the threshold conditions ruling the progression between the iteration levels. Our findings demonstrate the efficacy of the multilevel approach in accurately simulating graphene’s mechanical behavior, offering insights into its structural response across different scales.