To study dynamics processes, a mechanorheological viscoelastic-plastic model has been developed. It includes elastic, viscous, and plastic elements. Based on the experiments, a method designed to calculate the values of impact parameters was developed. A simplified model behavior was analyzed. It was assumed that under impact interaction, the model is viscoelastic-plastic since the beginning of the impact process, i.e., plastic deformations occur simultaneously with elastic ones. However, the experiments showed that at the loading stage, elastic deformations can occur as well. Under certain conditions, when stresses reach a yield point, plastic deformation occurs. The value of a control force for early development of plastic deformations can influence the duration and other parameters of the dynamic impact process. The experiments demonstrated that at the loading stage, the viscoelastic model becomes transformed into the viscoelastic-plastic one which increases the impact duration. It might be due to the fact that total deformations increase significantly owing to the plastic model component. As a result, the model motion value increases as well. Impact braking acceleration decreases, which leads to an impact duration increase. According to the results of the impact process research, the following conclusions can be drawn: the impact duration is influenced by the elastic-plastic transformation of the model. At the initial stage of plastic deformation, the force value is an important model control parameter influencing the impact duration and movement dynamics. The application of a more generalized model for solving practical tasks will help to increase research and impact interaction simulation accuracy and reliability.