This paper presents a new approach based on Extended Kantorovich Method to simulate the static response of micro-plates to electrostatic actuation. The presented model accounts for the electric force nonlinearity of the excitation as well as the applied in-plane loads. Using a one term Galerkin approximation and following the extended Kantorovich procedure, the nonlinear partial differential equation governing the micro-plate deflection reduces to two un-coupled nonlinear ordinary differential equations with constant coefficients which can be solved iteratively with rapid convergence to yield the desired solution. A parametric study has also been performed to characterize the effect of various design parameters such as applied in-plane loads and micro-plate aspect ratio to pull-in limits of micro-plates. Results in some specific cases have been validated, comparing them with other theoretical and experimental findings reported in the literature as well as the results of the finite element simulation of the problem. It is shown that rapid convergence, high precision and independency of initial guess function make extended Kantorovich method an effective and accurate design tool for design optimization of micro-plates under electrostatic actuation.