The present paper studies the problems of creation of techniques for the analysis of vibro-impact processes in systems with a large number of impact pairs. The used method of singularisation allows refusing from the ideas of the momentary impact and considering interaction hypotheses, which are more realistic than Newtonian ones. We consider the features of synchronous modes of movements of the clap type in systems with parallel impact elements as well as in tubes colliding with intermediate supports. Such modes are most dangerous in terms of the vibration wear of structural elements. The examples of calculation are given for specific designs.