Yielding shear panels, due to features such as ease of installation, replaceability, and high energy dissipation, are considered an economical solution for enhancing seismic performance. This study numerically and analytically investigated the seismic behavior of yielding shear panels. After validating the finite element model against experimental results, a set of 54 parametric models with two different heights was developed. The primary aim of these analyses was to evaluate the influence of key parameters, including slenderness ratio, opening percentage, and axial force, on seismic performance of these dampers. At the outset, the critical buckling load of the shear plate was calculated, and a fraction of this load was applied as axial force to the models. All analyses were conducted through nonlinear static procedures, and from the force–displacement curves, seismic indices such as elastic stiffness, ultimate strength, and energy dissipation capacity were extracted. Approximate equations were proposed based on curve-fitting techniques to estimate these results. The findings revealed that increasing axial force reduces both stiffness and strength, with the effect more pronounced in thicker plate models. Increasing the opening ratio by 20% led, on average, to reductions of about 28% in both strength and energy dissipation. Under an additional axial force corresponding to 16% of the critical buckling load, this reduction was further intensified, reaching 37% in ultimate strength and 36% in elastic stiffness. The proposed analytical equations not only provided acceptable accuracy but also demonstrated the capability to extrapolate and predict structural behavior within intermediate parameter ranges, offering a practical tool for design of such dampers.