An analytical model for the response of a reinforced concrete panel with friction energy dissipators is implemented for different input displacements. For this purpose, a hysteresis element based on an extension of the Bouc-Wen Model is developed. The hysteretic behavior includes the movement of steel anchor bolts inside small holes drilled in the RC panel, as well as the extension of the hole as a result of the impact. The analytical results show good agreement with the experimental results. A simple endochronic model is examined and it is discussed that the Bouc-Wen model could be looked at as a one-parameter endochronic model. These models violate the Il'iushin and Drucker postulates, however it is shown that this has an insignificant effect on the behavior of friction-type systems with small yield displacement compared to the maximum imposed displacement. An equation is developed to calculate the dissipated energy for hysteresis curves that are based on Bouc-Wen model over any time interval of stress or displacement that leads to nondecreasing time history of dissipated energy.