This paper considers the application of a nonlinear model of a dynamic shock absorber in building structures. The considered dynamic shock absorber forms a strained elastic rope with a concentrated mass on it. This dynamic shock absorber is structurally very simple and can be easily installed on various types of structures such as e.g. platforms, metal structures and other structures. The main advantage of such a dynamic shock absorber is the possibility to achieve its essential dynamic characteristics with the prestressing of the elastic rope (cable). The paper analytically and numerically considers the behavior of a model of a given structure that is exposed to different types of dynamic loading.