The problem of identification of conditions for fixing distributed mechanical systems by three natural frequencies of their oscillations is considered. Based on the Plücker condition arising when the matrix is reconstructed from its minors of maximal order, a set of well posedness of the problem is constructed and its A.N. Tikhonov well posedness is proved. For a wide class of problems an explicit solution of the problem of identifying the matrix of boundary conditions, written out in terms of the characteristic determinant of the corresponding spectral problem, is found. An example of a solution of a special problem from mechanics is given, as well as a counterexample showing that two natural frequencies generally speaking are not enough for uniqueness of the identification of boundary conditions.