Hollow structural sections (HSS) are widely used as braces because they have inherent axial, flexural, and torsional capacities. Delaying or preventing local buckling is accomplished by concrete infill in HSS braces to improve their cyclic response heavily relying upon three key parameters: (1) presence of concrete infill, (2) width (diameter)-to-thickness ratio, and (3) length-to-width (diameter) ratio impress the cyclic response of HSS braces. Nevertheless, it is not clear that based on which parameter, concrete infill can significantly enhance the peak compressive strength and energy dissipation capacity of HSS braces. This paper aims to investigate this concern while presenting a numerical study on the cyclic response of 120 HSS and Concrete-Filled Tubes (CFT) braces with various geometric characteristics. Square and circular cross-sections, 10, 12, 13.33, 20, 30, 33.33, and 50 width (diameter)-to-thickness ratios and 10, 15, 20, 25, 30, 37.5, 45, 50, 75, and 112.5 length-to-width (diameter) ratios are selected for the numerical investigation. Obtained results indicated that concrete infill can increase peak compressive and post-buckling strengths and energy dissipation capacity of HSS braces around 81%, 43%, and 73%, respectively. It was found that concrete infill and parameters of width (diameter)-to-thickness ratio and length-to-width (diameter) ratio influence the cyclic response of HSS braces differently. On the other hand, concrete infill noticeably enhances the peak compressive strength of HSS braces with larger values of width (diameter)-to-thickness ratio and energy dissipation capacity of such braces with lower values of length-to-width (diameter) ratio.