In this work, a nonlinear model to predict actuation characteristics in lateral electrostatically-actuated DC-contact MEMS switches is proposed. In this case a parallel-plate approximation cannot be applied. The model is based on the equilibrium equation for an elastic beam. It is demonstrated that the contribution of fringing fields is essential. The model relies on finite-difference discretization of the structures, applying boundary conditions and is solved with a Gauss- Seidel relaxation iteration scheme. Its usefulness is demonstrated in a series MEMS switch with lateral interdigital electrostatic actuation.