Recent experimental studies have demonstrated that the introduction of oxygen-containing functional groups in graphene sheets can greatly enhance the mechanical properties of their nanocomposites with polar polymers even at extremely low loadings. Motivated by these reports, we determine here the elastic constants of syndiotactic poly(methyl methacrylate) (sPMMA) at small wt % loadings of graphene sheets through atomistic modeling. To carry out a comparative study of the effect of graphene functionalization on the degree of mechanical reinforcement, we address both pure (i.e., unfunctionalized) and functionalized graphene sheets bearing epoxy and hydroxyl groups randomly bound on both sides of their surface in the host sPMMA matrix. The calculation of elastic constants (which involves no adjustable parameters) follows the methodology originally proposed by Theodorou and Suter [ Macromolecules 1986, 19, 139], and has been based on the use of the Dreiding all-atom force-field. Our predictions for the elastic constants (which for the pure sPMMA matrix are within the error bars of experimentally computed values) suggest a substantial increase in the elastic constants, especially in the case of functionalized graphene sheets. For example, at just 5.67 wt % loading of the host matrix in functionalized graphene sheets, they indicate an improvement in Youngs modulus E by similar to 74%, in the bulk modulus B by similar to 19%, and in the shear modulus G by 83%. Our results fully corroborate recent experimental measurements about the unique opportunities that functionalized graphene sheets offer for the design of new, very strong multifunctional materials at low nanofiller content.