Thin plates in semi-supported steel shear walls (SSSW) buckle under small lateral loads, and this buckling leads to deflection (out-of-plane displacement) in the plate. The onset of buckling at small lateral loads causes the wall plate to exhibit elastic post-buckling behavior over a wide range. For structural and architectural engineers, knowing the amount of plate deflection under different loads is crucial. Therefore, investigating the variation of lateral load with respect to the corresponding deflection in the elastic post-buckling region is of significant importance. In previous research, the von Kármán plate equations have been solved using the Galerkin method to obtain the displacement field of the wall plate in the elastic post-buckling region. Utilizing the ultimate shear capacity, a bilinear idealization of the lateral load-horizontal displacement curve of the wall has been approximated, and a relationship for the elastic stiffness of these walls has been presented. In this paper, using the results obtained from solving the von Kármán equations for different walls (variations in width, height, plate thickness, and changes in the secondary column), the deflection of the wall plate in the elastic region is obtained, and the load-deflection curve in this region is plotted. Furthermore, a practical relationship is presented for estimating the maximum elastic deflection of the wall plate (the maximum deflection corresponding to the first yield point of the wall plate), using machine learning and applying linear regression techniques.