Graphene has gained significant attention in recent decades owing to its exceptional mechanical and electrical properties, playing a crucial role in engineering nanotechnologies across various fields. However, investigating the mechanical properties of graphene experimentally poses considerable challenges due to its small scale, resulting in a scarcity of reliable experimental data in the literature. Consequently, harnessing the full potential of its remarkable characteristics requires accurate modeling methods. In this work, we propose a nonlinear molecular mechanics model and we integrate it into a finite element software to explore the size effect in graphene. Our simulations reveal that beyond a certain threshold size, the mechanical response of graphene ceases to be size-dependent, marking a transition from molecular to continuum modeling. Consequently, we develop a continuum hyperelastic model for graphene membranes subjected to plane deformations and lateral pressure, representing common stress states in practical nanotechnology applications. These models are based on nonlinear elasticity, providing a robust framework for accurately predicting graphene mechanics under real-world stress conditions.