This paper is concerned with systems consisting of components colliding with each other. In particular, a high velocity adiabatic impact cutoff machinę is investigated. For generał understanding of the impact dynamics (affected by a large number of parameters), the mech-anisms are modelled in a simplified and accurate manner. Two simple models are developed: the energy-balance model and the spring-mass model. The energy-balance model is based on the principle of total energy conservation. It provides only the punch minimum kinetic energy reąuired for efEcient cutting. Concerning the spring-mass model, the different components are represented by rigid masses and their deformations are modelled by springs (linear or non-linear in the case of contact stiffness). The resulting non-linear eąuations are solved using the Newmark numerical teclmiąue. The impact force, velocity, displacement and acceleration histories are calculated what makes possible a fine description of the cutoff cycle steps. The two models are helpful for both the design and tuning of the mechanisms involving impacts between their components.