In this contribution, an atomic force microscope is modelled and in this context, a non-linear coupled 3-D-boundary value problem is solved numerically using the finite element method. The coupling of this system is done by using the Maxwell stress tensor. In general, an iterative weak coupling is used, where the two physical problems are solved separately. However, this method does not necessarily guarantee convergence of the nonlinear computation. Hence, this contribution shows the possibility of solving the multiphysical problem by a strong coupling, which is also referred to as monolithic approach. The electrostatic field and the mechanical displacements are calculated simultaneously by solving only one system of equation. Since the Maxwell stress tensor depends nonlinearly on the potential, the solution is solved iteratively by the Newton method. © 2010 Author(s).