Abstract In this paper a new beam model of a micro-electro-mechanical resonator of power-law materials taking into account internal strain-rate damping of Kelvin-Voigt type is introduced and the corresponding lumped-parameter model is derived. Analytical formulas of the lumped-parameters in the model are presented. The pull-in solution is analyzed based on the lumped-parameter model. It is demonstrated analytically and numerically that the internal damping plays an important role in the pull-in solution as well as in determination of the amplitudes and frequencies of the resonator. The hysteresis loops are provided for this model with initial conditions using numerical simulations. The approximation of the electrostatic force in the lumped-parameter model is shown to give good approximations of amplitudes and frequencies relations with different values of the stiffness and damping coefficients.