The paper analyses the motion of mechanical systems, which causes simultaneous collisions (shocks) in their elements at more than two contact points. The main hypothesis, which is used in the theoretical calculations, is that the mentioned impacts begin and end at the same time at all impact contact points. Impact interaction of contact points includes normal reaction and dry friction force with correlations under stopping areas. Description of the relationship impacts at the same time at two, three or more points is given. For the description of the plane motion for mechanical systems the mass center motion theorem and the theorem of kinetic momentum changes are used. Acquired correlations are used in the mechanical systems plane motion analysis of transition and stationary motion regimes under a number of collision points. The modelling with MathCAD program is carried out for systems with one, two and three degrees of freedom, which takes place in collisions in two and more points. The inspection of theory has been performed by the Working Model 2D Program for mechanical systems with one, two, three degrees of freedom with collisions at three or more points. Validation of studies is significant. In addition the demonstration results for experimental studies for vibro drive system are given. Accordingly, the vibro engine is created by disbalance motors of the pendulum platform in plane motion. Impacts are generated in two flat springs after rotation abruption from fundament. The results of the work may be used in calculations of equipment in the mechanical positioning system, as well as in the design of new mechanisms or machines, such as vibro conveyors or vibro engines.