Using molecular mechanics simulations, we investigate the deformation mechanism of graphene monolayer under free standing indentation. During indentation, the van der Waals (VDW) interaction between the indenter tip and graphene monolayer will cause: (i) a phase lag between the indentation force P and the indentation displacement δ (i.e., δ>0 when P=0); (ii) a different strain energy function than that in in-plane tension; (iii) a larger nonlinear deformation than its counterpart in in-plane tension. Thus, the elastic properties of graphene monolayer (including the second-order elastic stiffness E and the third-order nonlinear elastic constant cmi) determined by free standing indentation are different than those determined by in-plane stretching, especially for cmi. The VDW effect rapidly decreases with the increase of the indentation load. Under a small load (i.e., in-plane strain ε⩽2.5%, typically used in the real tests), the classic indentation analysis cannot give the correct results, especially for cmi. Under a large load (e.g., ε increases to 5%), the error caused by the classic indentation analysis can be effectively reduced. Therefore, the deformation mechanism must be understood in order to accurately determine the elastic properties of graphene from free standing indentation.