A theoretical model for the dynamic behaviour of a soil compaction tamping machine is derived. The Matlab toolbox Simulink is used to solve the equations of motion. Simulink is used because it is possible to combine the kinetic model of the machine with a more complex FE-model. The theoretical model has been verified experimentally, where the soil compaction tamping machine was run on a simulated soil material. The agreement between the simulation and the experiment is very good, which implies that this simplified model of the machine can be used for a more complete study of the total system, including a more correct soil model.