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Any mechanical multibody system consists of elastic elements to a smaller or greater extent. The rigid elements hypothesis, generally performed when studying such technical systems, represents a first approximation in the dynamic analysis. This hypothesis may be satisfactory or not depending on the specific operation conditions of the mechanical systems. If the velocities and the occurring loads are low then the rigid elements hypothesis can lead to an excellent model. But if the velocities and/or the occurring loads are high, the elasticity becomes a significant element and the deformations may have generally an unfavorable influence on the operation of such a system. The phenomena of resonance and loss of stability also represent elasticity forms of manifestations and may also occur in such a system. In the paper are presented the motion equations for a such system and an application to the interaction chambre of a gamma ray beam.