<p>The study focused on the numerical and analytical evaluation of Non-uniform Slit Dampers (NSDs). An experimental sample was utilized to calibrate the numerical model. Analytical equations were presented for calculating the elastic stiffness of the damper, and a simplified approximate equation was also provided. Nonlinear cyclic analyses were conducted to examine the impact of damper dimensions on energy dissipation, strength, effective stiffness, and equivalent damping ratio (EDR). Subsequently, approximate equations based on curve fitting methods were proposed for easier calculation of these results. In the second part of the study, the buckling load of the damper was calculated using the Rayleigh-Ritz method. Then, the effect of applying 3–12% of this load on the stiffness, strength, and ductility of the NSD was evaluated. The results showed that decreasing the height, increasing the width, and the mid-width of the damper led to an increase in energy dissipation. When a plastic hinge formed in the weakened section, reducing the mid-width of the damper led to an increase in EDR. An increase in the axial force applied to the damper caused a reduction in elastic stiffness, strength, and ductility, with the effect being more pronounced as the mid-width of the damper decreased.</p>