In this paper, a monotone positive solution is studied for buckling of a distributed model of multi walled carbon nanotube (MWCNT) cantilevers in the vicinity of thin and thick graphite sheets subject to intermolecular forces. In the modeling of intermolecular forces, Van der Waals forces are taken into account. A hybrid nano-scale continuum model based on Lennard–Jones potential is applied to simulate the intermolecular force-induced deflection of MWCNT. A positive monotone solution based on Green’s function in the form of a nonlinear iterative integral is introduced to obtain a solution for deflection of MWCNT cantilevers. In order to determine the accuracy of the presented method, the results are compared with numerical results of a numerical method as well as other methods reported in the literature. The results show that the monotone iterative solution is stable and converged to numerical results with a few iterations. The results of the present work are useful to prove the stability and convergence of Green’s function to deal with deflection of nano cantilever actuators in future works and simplifications.