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The classical Euler–Bernoulli beam model and Kirchhoff plate model are very useful on the macroscopic scale. In the context of Eringen’s nonlocal elasticity theory, this article aims to develop the criteria of the applicability of nanoscale Euler–Bernoulli beam and Kirchhoff plate models based on the Timoshenko beam model and the Mindlin plate model via the wave propagation theory. The corresponding governing differential equations for the nanoscale Timoshenko beam and Mindlin plate are derived by the Hamilton’s principle, and the dispersion equations of wave are then obtained. By applying Taylor expansion to the corresponding solutions of the dispersion equations, new criteria are developed, simultaneously taking into account the effects of nonlocal parameters and material properties. When the nonlocal parameter is set to zero, the present criteria may be readily degenerated to their macroscopic counterparts. According to the present criteria, this article systematically evaluates the existing studies in literature. Various works in literature did not consider the effect of the nonlocal parameter, and hence, failed to satisfy the application conditions of the Euler–Bernoulli beam and Kirchhoff plate models on the nanoscale. The work in this article is of scientific significance to various studies on nanostructures.

New criteria for nanoscale slender beams and thin plates: Low frequency domain of flexural wave