Inverse problem is a kind of problem that "effects" are used to get the "causes". It has broad application prospects in the field of applied mathematics and physics. The paper makes an inversion analysis based on a cantilever beam via polynomial model. An iterative formula is deduced based on Gauss-Newton method to tackle inherent parameter of cantilever beam. In the process of inversing, direct problem is solved for many times. The polynomial model is constructed and taken as a direct problem solver. The method proposed in this paper can make parameter inversion of cantilever beam with variable Young's modulus. The result shows that the method has good stability. It can give some guidance for engineers to solve other inversion problem in engineering. © 2019 IOP Publishing Ltd. All rights reserved.