We focus primarily on the conceptually new class of materials that are only one atom thick, called by common name “graphene”. The experimental measurement of the mechanical properties of graphene is still considered a difficult task, thus quantifying the mechanical properties by the numerical simulations is of great importance.rnWe use molecular mechanics and assume that atoms are the smallest unit needed to be modelled. Due to the lack of computational power, performing a fully atomistic simulation of practical carbon nanosystems is not always possible. Thus, we seek to find more effective modelling strategy which considers the development of the substitute, continuum model of pristine graphene in the small and large strain regime. Next, we turn to concurrent multiscale methodology which limits atomic model to a small cluster of atoms near the defect in graphene lattice based on the overlapping domain decomposition scheme and coupling of discreet and continuum models. The latter enables to have efficient continuum model, preserving at the same time the accuracy of atomistic model.rnContributions : main mechanisms resulting in a large dispersion of elastic properties are identified, the novel elastic stiffness bounds in the equivalent continuum modeling of graphene are developed , novel hyperelastic constitutive model in terms of principal stretches for large elastic strain regime is developed, a unified coupling formulation of the atomistic-to-continuum coupling is proposed.