The elastic modulus and Poisson’s ratio of polymer matrix nanocomposites (PMNCs) filled with graphene nanoplatelets (GNPs) are determined using an analytical micromechanical model. It is assumed that the GNPs are uniformly dispersed and randomly oriented into the polymer matrix. Due to the folded and wrinkled structure of GNPs, the effect of their flatness ratio on the elastic properties is investigated. Moreover, the micromechanical model captures the creation of interfacial region between the graphene and polymer matrix. The results show that addition of graphene particles into the polymer matrix can enhance the nanocomposite elastic modulus. Poisson’s ratio of polymer matrix increases with the increase of graphene content. It is observed that the elastic properties are decreased by the GNP non-flatness structure. Also, the material and dimensional characteristics of interfacial region affects the elastic modulus and Poisson’s ratio of GNP-reinforced PMNCs. The model predictions agree very well with the experimental data.