The effects of the degree of functionalization, molecular structure and molecular weight of functional groups on the Young's modulus of graphene sheets were investigated through molecular dynamics and molecular mechanics simulations. The dependence of shear modulus, strength and critical wrinkling strain of graphene sheets on the chemical functionalization was also examined. It is found that Young's modulus depends greatly on the degree of functionalization and molecular structure of the functional groups, while the molecular weight of the functional groups plays a minor role in determining Young's modulus. The chemical functionalization also reduces the shear modulus and critical wrinkling strain. The binding energy between the functional groups and the graphene sheets is mainly responsible for these findings. © 2010 Elsevier Ltd. All rights reserved.