In this paper, an analytical solution of the equation of motion in the displacements of the sensing element of a nanoelectromechanical sensor is obtained. The equations of motion were obtained using the dynamic principle of virtual displacements, the third-order plate bending theory, and a new modified couple stress theory. The components of the displacement vector and the linear dimensions of the plate normalized by the value of the plate's height. The sensitive element of the nanosensor was considered as a size-dependent orthotropic plate, simply supported at the edges and under the distributed load. The deflection of the plate is represented as a double trigonometric series. The obtained results were compared with the results of numerical modeling of microplates, carried out in one of the well-known finite element modeling software. Also in work, the influence of size-dependent parameters on the deformation of the nanoplate was analyzed.