Timoshenko beam theory is utilized to develop the governing equation of vibration of the nonlocal nanowires using the energy method and Galerkin procedure. The potent and well-known Variational iteration and Homotopy perturbation methods are used to find the analytical solutions of the oscillation of the nanowires. A closed-form solution is obtained for the natural frequency of the system. It is very important to obtain the frequency-amplitude formulation of the nano-scale system due to their sensitivity to very small oscillations. The focus of this work is to obtain the frequency-amplitude relationships of the vibration of the nanowires and also investigate the effects of different parameters on the dynamical behavior. The sensitivity of the natural frequency of nanowires to the variations of the surface effect, transverse shear deformation and the aspect ratio is investigated. Furthermore, the effect of variations of amplitude on the nonlinear oscillation of the nanowires is examined and the influence of the nonlocal parameter on the dynamical behavior of the nanowires is studied. Two different types of the cross-sectional area, namely the rectangular and the circular nanowires were considered and the effects of all the above-mentioned parameters have been examined. Eventually, numerical simulation methods are performed to delineate the accuracy of the results obtained by means of the variational iteration and the Homotopy perturbation methods.