The basic purpose of given article is consideration of the problems connected with application of a method of concentrated weights in the tasks of mechanical sys-tems dynamics at non-classic internal and external constraints. The method of the concen-trated weights is convenient means of the analysis of dynamic properties of elastic mechanical systems. It has relative simplicity of definition of the parameters of equivalent discrete system, the clearness of computing algorithms and provides comprehensible accu-racy of definition of the lowest natural frequencies. Doubtless advantage of a method is convenience of modeling of non-classic constraints of fastening and internal constraints be-tween elements of complex systems. Such problems arise at the decision of practice tasks of the analysis of dynamics of real systems. The method is used for the analysis of vibrations of a beam with variable parameters at presence of elastic supporting of the beam and the attached additional concentrated weight. A result of dynamic analysis has a good corre-lation with the fatigue damages observed at fatigue test of a beam.