Using molecular mechanics simulations, we investigated the true pre-stress/pre-strain state of graphene in free standing indentation and the effect of the pre-strain (ε0) on the free standing indentation response of graphene is also considered. We found that there is essentially no effective pre-tension in graphene during free standing indentation and the reported pre-tensile stress determined from the indentation tests does not show the true pre-stress state of graphene, which is a 'fake stress' caused by the assumption (the indenter tip displacement is equal to the displacement of graphene) typically used in the classic indentation analysis. A negative ε0 will increase the van der Waals (VDW) interaction between the indenter tip and graphene to cause a larger overestimation of both values of the elastic modulus (E) and the nonlinear elastic constant (c) of graphene from the classic indentation analysis. However, applying a positive ε0 in graphene, the VDW effect will be significantly decreased, and a more accurate value of E can be obtained, but the value of c will decrease to zero, which may become an effective way to more accurately obtain the elastic stiffness of graphene from indentation tests.