This paper compares the use of two impact simulation methods for two-degree-of-freedom nonlinear vibroimpact systems with rigid and soft impacts. These methods are (I) impact simulation by boundary conditions with the use of Newton's restitution coefficient based on stereomechanic shock theory and (II) impact simulation by contact interaction force based on quasistatic Hertz's contact theory. It is shown that both methods are applied and give the coinciding results for system with elastic rigid impact under periodic external loading. Loading curves built by parameter continuation method are confirming this result. Impact simulation by the second method is also fulfilled for vibroimpact system with rigid impact under random external loading. For vibroimpact system with soft impact, the simulation of impact by the second method gives a better result. The application of linear elastic force as contact one is possible too but the use of Hertz's contact force is more preferable. The authors consider that the impact simulation by Hertz contact interaction force gives good results for nonlinear vibroimpact systems with impacts of any kind if all limitations with Hertz's law used are observed. 1. Introduction Impact and vibroimpact devices are widely used in engineering. Their use is described convincingly and in detail in [1]. Therefore vibroimpact processes dynamics in mechanical systems is the investigation subject of special interest that predetermines study of motion and contact interaction forces between bodies in vibroimpact systems. Such investigations are developed extensively during the last 50 years. Many monographs and papers were devoted to this topic, for example, well-known monographs [2–4]. But one can face the big difficulties while solving some real and several theoretical tasks. And impact processes investigations are continued at the present too. Among the contemporary publications we want to underline such encyclopedic works as Ivanov’s [5], Ibrahim’s [6], and Stronge’s [7] monographs. A big attention is paid to stability studying in systems with impacts, periodic motions bifurcations, grazing bifurcations, singularities at vibroimpact dynamics, and other specific problems [2, 8–12]. Let us note by a way that Ibrahim’s research monograph [6] is followed by the list of over 1100 references! From our point of view the question about impact simulation way, that is, the impact rule, is not of little importance in the time of the vibroimpact processes dynamics investigations. Ivanov in [5] writes; “The choice of this or other impact model for
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