Two-dimensional nano-materials such as graphene and hexagonal boron nitride nano-sheets Fig.1 have attracted tremendous interest in the research community and starting-point for the development of nanotechnology. Using classical applied mathematical modeling, we derive explicit analytical expressions to determine the binding energies of noble metals including copper, silver, gold, platinum and Iridium (Cu, Ag, Au, Pt and Ir) atoms on graphene and hexagonal boron nitride nano-sheets, as shown in Fig.2 . We adopt the 6–12 Lennard-Jones potential function together with the continuous approach to determine the preferred minimum energy position of an offset metal atom above the surface of the graphene and hexagonal boron nitride nano-sheets. The main results of this study is an analytical expressions for the interaction energies that we then utilize to report the mechanism of adsorption of the metal atoms on graphene and hexagonal boron nitride surfaces. Results observe that the minimum binding energy is occured when Cu, Ag, Au, Pt and Ir are is set at a perpendicular distances in the region from 3.302 ˚A to 3.683 ˚A above the nano-sheet surface which correspond to an adsorption an adsorption energies in the region from 0.842 to 2.978 (kcal/mol). Our results might assist to provide the main information on the interaction energies between the metal atoms and the two-dimensional nano-materials.