The modelling enables analysis of various design solutions even in the design phase, and makes it possible to study the influence of specific design parameters on the performance of the machine designed. Mathematical models representing the dynamics of the hand-arm system, together with models of impact tools, enable simulation analyses and determination of the construction features of the tool. This paper discusses the harmful influence of vibration on human operators and the danger of the Vibration Syndrome. It also presents a description of a soil compacting tool constructed at the Chair of Machine Design Fundamentals at the Poznań University of Technology, as well as single and multi-mass mathematical models of dynamic properties of the vibration isolator, including models of the operator's hand and the soil compacted. Additionally, the paper discusses the results of simulation analyses of the selection of specific parameters of vibration isolation systems for pneumatic tools. The mathematical models enable the design of vibration isolators of high dampening efficiency for the vibration transmitted into the human body, without loss of technological efficiency of the actual technological operation.