The　size-dependent　mechanical　response　of　graphene　is　investigated　with　an　entirely　nonlinear　molecular　mechanics　approach.　Finite　element　(FE)　simulations　under　uniaxial　and　equibiaxial　tensile　loads　are　carried　out　on　graphene　sheets　with　increasing　size.　It　is　found　that　the　response　of　graphene　remains　unchanged　after　a　threshold　size.　Furthermore,　anisotropy　is　observed　for　large　deformations　and　a　negative　Poisson＇s　ratio　is　found　after　a　critical　strain　for　the　zigzag　uniaxial　load　case.　The　threshold　size　defines　the　transition　to　the　continuum　theory,　which　is　developed　as　a　membrane　model　in　the　fully　nonlinear　context　of　finite　elasticity.　The　constitutive　parameters　of　the　model　are　calibrated　by　fitting　the　results　of　the　FE　simulations.　The　proposed　model　represents　the　basis　for　accurate　predictions　of　the　response　of　graphene　subjected　to　large　in-plane　deformations.　Nonlinear　laws　for　the　size-dependent　elastic　properties　of　graphene　are　derived.　These　laws　can　be　used　in　linear　elasticity-based　models　to　take　into　account　for　material　nonlinearity,　anisotropy　and　size　effect.　Finally,　a　sensitivity　analysis　of　the　molecular　mechanics　model　to　the　parameters　of　the　interatomic　potentials　is　carried　out.　The　discussion　of　the　results　gives　insights　into　the　influence　of　each　parameter　and　useful　remarks　for　the　molecular　mechanics　modeling　of　graphene.　©　2021　Elsevier　Ltd