This paper is a part of research in searching an appropriate damper for space structures constructed in seismic areas. The study investigates a stiffness, strength and energy dissipation of the damper under loading. For this purpose, a U-shaped hysteresis steel damper is modeled and analyzed by a nonlinear finite element technique which involves both geometrical and material nonlinearities. The model is subjected to a monotonic increasing load which is applied horizontally until one cycle of hysteresis is formed. The stiffness, strength, and energy dissipation of the damper is directly determined from the graph of load-displacement. Feasibility of the hysteresis damper is investigated further for application on building construction. The damper is placed on the roof and supporting structure of the building. A 2-DOF spring-mass model, as a simple modelling of the building is introduced with damper's properties are taken from the results of the first study. A seismic load is applied to see the response of the model. The static numerical analysis showed that the properties of the introduced damper, such as stiffness, strength and energy dissipation, are depending on the geometry of the damper. The results show that reducing the length of lower plate or height of the damper will increase stiffness, strength and energy absorption. In contrary, reducing the width of the damper will decrease all properties. Moreover, the results of the dynamic analysis show the feasibility of damper to reduce to reduce the amplitudes of the response of the roof under seismic load.