In this paper, the equivalent linearization method with a weighted averaging is applied to analyze nonlinear vibration of Euler-Bernoulli beam resting on the elastic foundationand subjected to the compressive axial force. Frequency-Amplitude relationships of beams with simply supported and clampedclamped end conditions are given in closed-forms. The present results are comparedwithonesachieved byusing He�s Variational Approach method and the 4th-order Runge-Kutta method, comparison shows accuracy of the obtained solution. Effects of the compressive axial force and the coefficient ofelastic foundation on the nonlinear vibration behavior of beam are investigated in this work.