Summary: ``Micromechanical electronics sensors are widely used in various fields of science and technology. The automotive industry, marine and space techniques, navigation equipment, military vehicle, consumer electronics, robotics, smart systems---this is not a complete list of areas, in which these sensors are used. Nanoelectromechanical sensors (NEMS) are the next step of evolution of micromechanical electronics sensors. Due to the nanosized of sensing elements and other components of NEMS, they need non-classical approaches for the study of their dynamics. One more problem of NEMSs is the dependence of their characteristics on material anisotropy or orthotropy. In the article, equations of motion of a sensing element of micro- and nanoelectromechanical sensors as an anisotropic size-dependent plate were obtained based on the modified couple-stress theory. The sensing element was considered as rectangular console plate under the distributed force at the bottom of the sensing element. The dynamic version of the principle of virtual displacements and the third-order theory of laminated composite plates and shells were used for obtaining the differential equations of motion and natural boundary conditions.''