<p>High-order theory for curved nanorods and straight nanobeams has been developed based on the expansion of two-dimensional (2-D) nonlocal elasticity equations into a series of the Legendre polynomials in terms of a thickness coordinate. Thus, all elasticity equations including the generalized Hooke’s law have been transformed into the corresponding equations for the expansion coefficients in the Legendre polynomials. System of differential equations for displacements in terms of the expansion coefficients in the Legendre polynomial has been obtained. The developed models have been used to simulate electrostatically activated NEMS using commercial software Mathematica 14.0. The phenomenon of pull-in instability of nanobeams with various geometric and microstructural parameters has been studied using models of nanobeams of different orders including the Timoshenko model.</p>