Abstract: In this present paper, an approaching method of centripetal-load models for solving Beck's problem is proposed. The methods is to transform Beck's column into a series of centripetal-load models which are equivalent to Beck's column under some conditions. The follower forces of Beck's column corresponding to different frequencies, and conversely, the frequencies to different loads may be obtained through iterative calculations. The convergence characteristics of the method are analysed and some numerical results are provided in the paper.