In the present work, an extensive study for predicting efficiency parameters (��i) of various simulated nanocomposites including Polymethyl methacrylate (PMMA) as matrix and different structures including various sizes of graphene platelets (GPLs), single, double, and multi-walled carbon nanotubes (SWCNTs-DWCNTs-MWCNTs), and single and double-walled boron nitride nanotubes (SWBNNTs-DWBNNTs) are investigated. It should be stated that GPLs, carbon and boron nitride nanotubes (CNTs, BNNT) with different chiralities (5, 0), (5, 5), (10, 0), and (10, 10) as reinforcements are considered. In this research, molecular dynamics (MDs) method with Materials studio software is applied to examine the mechanical properties (Young's modulus) of simulated nanocomposite boxes and calculate η1 of each nanocomposite boxes. Then, it is noteworthy that by changing length (6.252, 10.584, and 21.173 nm) and width (7.137, 10.515, and 19.936) of GPLs, ��1, ��2, and ��3 approximately becomes (0.101, 0.114, and 0.124), (1.15, 1.22, and 1.26), (1.04, 1.05, and 1.07) respectively. After that efficiency parameters of SWCNTs, DWCNTs, and MWCNTs are calculated and discussed separately. Finally efficiency parameters of SWBNNTs and DWBNNTs with different chiralities by PMMA as matrix are determined by MD and discussed separately. It is known that the accurate efficiency parameters helps a lot to calculate the properties of nanocomposite analytically. In particular, the obtained results from this research can be used for analytical work based on the extended rule of mixture (ERM) in bending, buckling and vibration analysis of structure in future study.