This paper is concerned with the free vibration problem for micro/nano beams modelled after Eringen’s nonlocal elasticity theory and Euler beam theory. The small scale effect is taken into consideration in the former theory. The natural frequencies are obtained using the Hamilton’s principle and Chebyshev polynomial functions. The present method, which uses Rayleigh–Ritz technique in this paper, provides an efficient and extremely accurate vibration solution of micro/nano beams where the effects of small scale are significant. Numerical results for a variety of some micro/nano beams with various boundary conditions are given and compared with the available results wherever possible. Through the comparison of the results and the appropriate discussion, the knowledge of the level of capability of the developed method is promoted.