Abstarct: Micro-electro-mechanical systems mostly made baxsed on silicon and its derivatives tended to other materials such as polymers and rubbers. Elastomers, between polymeric materials, investigated in this study due to their special properties, specially their rubberic behavior. Dielectric elastomers have simple structure consisting of elastomer and parties electrodes, so they have capacity behavior. This feature, along with other features such as high strain, flexibility, compliance with environmental, quick response introduces elastomers as highly desirable material in a variety of applications of artificial muscles, clamps, sensors and resonators. In this thesis, the dynamic behavior and vibrating mechanical member of microelectromechanical systems made of this material will be studied using Hayprelastic models. These models anticipate rubberic behavior and nonlinear relationship of stress and strain in these materials, well and with selecting these models properly, we can involve material nonlinearity in addition to other factors. In the first chapter of the thesis, we present some preliminaries such as micromechanical systems, elastomeric materials with desired applications and advantages of them, an overview of the mechanical properties of rubber, hayperelastic materials (expressing non-linear elastic behavior) as well as models, types of stimulation that is used in the dielectric elastomers. In the second chapter a comprehensive overview is done about the researches being done in this area. Free and forced vibration of micro-beam and micro-plate for classical Euler-Bernouli and shear theories with considering Yeoh and Biderman hyperelastic models will be studied in the third chapter. Meanwhile, the effects of various parameters such as mode number, length, thickness and aspect ratio on frequency will be investigated. In addition, we apply modified couple stress theory to consider size effect and its results with diminishing length scale parameter will be compared with classical theory results. Pull-in stability for Yeoh and Biderman models and critical magnitudes of voltage, nominal electric field and stretche ratio will be achieved. In addition to the proposed model, we consider different configuration with one electrode on top and another fixed electrode with a gap from bottom surface. Dynamic behavior of this microbeam, pull-in voltage and deflection will be investigated with one mode analysis for two different voltages under electrostatic actuation.