Fast dynamic processes of material compaction by vibration rollers represent random dynamic processes, wherein characteristics of the strength of compacted material, humidity, temperature, types of materials and their characteristics change stochastically. However, from the total set of these processes it is possible to single out such processes, which belong to the category of random ones because of their insufficient state of knowledge but they are deterministic. Such processes may include the vibratory drum dynamic vertical movements during the material compaction. In the process of the study the vibratory drum downward and upward movement modes are considered under the action of the dynamic driving force, which while projecting onto a vertical axis turns into a harmonic force acting periodically downwards and upwards and it is a deterministic parameter. Other mass and kinematic characteristics of the vibratory drum are also deterministic ones. On the basis of classic laws of dynamics the vibratory drum bouncing dynamic processes in the final stage of the compaction technological process and accompanying process of the vibratory drum vertical downward movement have been analytically considered. The necessity to solve such problem is justified by the fact that the dynamic process parameter determination by experimental methods is connected with significant physical and material expenses. New knowledge has been obtained that is necessary for the improvement of the vibration roller designs and modes of their operation.