Closed form expressions are obtained for the dynamic response of a micro-scale elastic beam in this paper. The nonlinear governing equation of motion is derived and solved using the Variational Iteration Method (VIM) and the Energy Balance Method (EBM). The frequency responses are presented in closed forms and their sensitivities with respect to the initial conditions are investigated. A number of numerical simulations are then carried out and the performance and validity of the solution procedure are evaluated in the time and frequency domain as well as in the phase plane. Accuracy of the solution procedure is studied by comparing the obtained results with those obtained from the exact solutions. Different effects of the nonlinear parameters and initial amplitude on the natural frequencies are also investigated in a parametric study. It is proved that VIM and EBM are simple and reliable techniques to solve the corresponding nonlinear differential equation.