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Several advantages of yielding dampers in controlling seismic energy have attracted the attention of many researchers in designing new buildings and retrofitting existing structures. In recent decades, various shapes and substances of such dampers have been used in engineering structures and their behavioral features, including the energy dissipating capacities, have been assessed. In this article, a novel method is presented to obtain the design relationship of two types of yielding elliptical dampers in terms of their selected geometric properties, i.e. distance between the shear diaphragms or virtual diameter and thickness. In addition, two different ellipticalshaped steel dampers equipped with the shear diaphragms are proposed and modeled using the finite element software ABAQUS and their performances are investigated. Then, 30 and 25 models, respectively, of the first and second types are studied using pushover analysis. The designed dampers considering the proposed relationships are used in two chevron braced steel frames placed between the bracing and the beam. Due to their desirable efficiency in energy dissipation and increase in the equivalent viscous damping of the frame, better efficiency is achieved in the modified damper with easier fabrication. [ABSTRACT FROM AUTHOR]