Exact analytical solutions of the problem of free oscillations of orthotropic cuboid with free edges, based on the use in all three directions of trigonometric functions as basis. It was found that the solution described purely bezsdvigovye waveforms that occur in the body in question at a specific aspect ratio of the parties and the physical and mechanical characteristics of the material. It is shown that in the limit to zero harmonics in one or two directions, as well as zero values of four of the six or all of Poisson’s ratios built solutions are reduced in such precise solutions that match the use of the equations of classical theory of plates Kirchhoff or rod theory Kirchhoff-Clebsch. The presence of the bodies at such frequencies of free oscillations, which in certain proportions of its geometrical and physical and mechanical properties well below known.