<p>Yielding dampers should be designed in such a way that before the main elements of the structure yield, they provide the possibility of energy absorption and consumption. Therefore, for the structure’s basic design, the damper’s behavior in pressure and tension should be known, and their effect on the stiffness and strength of the structure can be estimated with relatively simple relationships. The main purpose of this paper is to provide accurate analytical relationships for the behavior of tubular dampers in compression and tension under the effect of uniform loading. In this regard, firstly, the behavior of a circular yielding damper was evaluated based on validated numerical models in ABAQUS software. Then, analytical relationships that show high accuracy compared to the results of finite element modeling have been presented using linear and nonlinear analysis. Also, a new bolt and nut connection detail is provided to reduce the possibility of welding failure at the joints of circular dampers. The new detail has been tested at a full-size scale and has shown no failure at the weld, even at large displacements. In the end, the results of the experimental sample with the presented analytical relations have shown that the analytical relations are highly accurate.</p>