Abstract: A method to estimate the system natural frequencyusing the unit natural frequency is developed by deriving the relationbetween thefirst order natural frequency of the frame structure and that of a simple framestructure. The method in this paper is verified through ANSYS, byusing the finite elementmodal analysis. The calculation for the derrick of an oil drilling rigshows that the erroris not exceeding 1\%. It is shown that the method is convenient andfeasible for the natural frequency estimation of frame structures in series.