In seismic areas, the application of structural dampers becomes compulsory in the design of buildings. There are various types of dampers, such as viscous elastic dampers, viscous fluid dampers, friction dampers, tune mass dampers, yielding/ metallic dampers, and magnetic dampers. All damper systems are designed to protect structural integrities, control damages, prevent injuries by absorbing earthquake energy, and reduce deformation. This paper is a part of research investigating the behaviour of the U-shaped steel damper (as one type of metallic damper) that can be applied to the buildings in seismic areas. The dampers are used as connections between the roof and supporting structure, with the two general purposes. The first is to control the displacement of roof under an earthquake, and the second is to absorb seismic energy through the plasticity of some parts in dampers. If a strong earthquake occurs, the plasticity will absorb the seismic energy; therefore, heavy damage could be avoided from the roof’s mainframes. In this paper, several models of U-shaped steel dampers are introduced. Several parameters, such as elastic stiffness, maximum strength, and energy dissipation, are determined under two conditions. Firstly, static analysis of the proposed damper under variation of U-steel plate configurations, searching the model with more significant energy dissipation. Secondly, static analysis of the unsymmetrical and symmetrical damper under different loading directions. An in-house finite element program that involves both geometrical and material nonlinearities is developed as a problem solver. A quasi-static lateral loading is given to each model until one cycle of the hysteresis curve is reached (in the displacement range between -20 mm to +20 mm). The above parameters are calculated from the hysteresis curve. From the results, the behaviour of the U-steel damper can be described as follows. Firstly, increasing the energy dissipation in the lateral direction can be done by increasing the lateral stiffness of the damper. However, it can reduce the maximum elastic deformation of the damper. Secondly, under the random direction of loading, a symmetrical shape can increase the energy dissipation of the damper.