This book presents an attempt of the author at systematizing the work devoted to multi body vibration system mechanics and to highlight the application of the models in science and technology. Vibrations are considered in two main directions: first, as a technological useful motion in industry, where vibrations are generated and controlled by means of a suitable system adjustment and second, as a harmful vibration shock loading, where active and passive vibration isolation is needed. The book is structured in three main parts dealing with single, double and three mass vibration mechanical models, respectively. The objective of the work presented here is creation, investigation and control in plane and space of mono-frequency and poly-frequency vibrations of multi body system vibration mechanical models and their application in vibration technics, science and technology. Author highlights some of the up-to-date scientific and technical problems, as well as some technically applicable software, widely used in the engineering community worldwide and of course, the author will be very happy if the investigations give some thoughts and are used as a basis for some future research.