In the paper,the dynamics equation of the elastic beam rotating around a fixed axis is transferred to the state equation,based on the p recise computation of exponential matrix and direct integral of primitive functi on,a new computational scheme is presented to calculate the natural frequencies of the beam.The method has a higher precision than other methods previously adop ted and also can be applied to computing non-uniform beam with effecting of axi s force.In the given example,the first and second order natural frequencies with their stiffing coefficients are computed for rotating elastic beams which diffe rent mass on its free end.The result is shown that heavy mass has less effect on the first natural frequency than the light mass,but it is reverse on the second .