Abstract: In this paper the problem was discussed in which the flextural rigidity and density of the Euler-Bernoulli Beam were solved from some of the displacement modes or the strain modes and the corresponding frequencies of a cantilever or a pinned-pinned beam. The necessary and sufficient conditions for the unique ex istence of a solution to the problem have been set up. An algorithm was proposed and numerical calculations were carried out. Examples and analysis both showed that much better results could be attai...