<p>The use of Variable Grooved Plate Dampers (VGGPDs) in cross-braced frames has recently demonstrated significant effectiveness as a reliable system. The damper plate is divided into four parts, with specific thicknesses or lengths assigned to the upper and lower parts, and distinct specifications applied to the middle parts. Theoretical and parametric studies have demonstrated that the optimal variable ratio for each configuration, in terms of the length and thickness ratio of the strips, is approximately 1.5. In this paper, a comprehensive model capturing the nonlinear behavior of the VGGPD system incorporating strength degradation region was developed. The analytical results obtained from the proposed model were then compared with the published experimental and numerical data for selected specimens, showing a high level of agreement with discrepancies of less than 10%. Furthermore, the connector element feature in ABAQUS was employed to model the damper using the obtained analytical equations that describe its force-displacement characteristics. The results demonstrate that this method accurately represents the nonlinear and hysteretic behavior of the damper under cyclic loading. Therefore, the practical application of this damper is feasible, and it can be included in the relevant building codes as a new lateral load-resisting system classified as a supplemental special concentrically braced frame with enhanced performance requirements.</p>