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This paper reports on a numerical algorithm for quasi-static dynamic modeling of highly nonlinear electrostatic actuators with single-side clamped moving elements, such as curved-electrode actuators or zipper-like touch-mode actuators. The algorithm is capable of simulating pre-stressed materials and touching surfaces with complex geometries of the moving and the rigid structures, including stoppers and thickness variations of the moving parts. In contrast to conventional, very time-consuming simulation methods, the proposed algorithm takes only a fraction of a second which makes it a very powerful design tool for parameter-optimization of the actuator geometry. The paper describes the algorithm, implemented in MATLAB, and reports on its performance evaluation, comparing its simulation results with those obtained by other methods such as simplified analytical models, FEM/BEM/FCM/BCM simulations and measurements of fabricated structures, including laterally moving MEMS switches and vertically closing pre-stressed thin-film zipper-actuators. The algorithm shows good agreement with measurements and results obtained by these methods.