Research of natural vifrations of anisotropic composite box beams are an interesting practical problem, which previously was not discussed in detail. The authors of previously published works, as a rule, are generally limited to the consideration of the two-three lower vibrations’ modes. Such a small number of modes analyzed does not allow an overall picture arising in such structures modal interactions involving multiple mutual transformations. The latter circumstance was the reason for writing this paper. Its first part contains a detailed description of the mathematical model of the problem, while the second part shows the results of calculations and their detailed discussion. Refs 11. Figs 2