A Semi Supported Steel Plate Shear Wall (SSSW) is an emerging structural system used to resist lateral loads in buildings. In this system, the steel wall plates connected to secondary columns undergo buckling under small lateral loads, leading to out of plane deflection. Because buckling initiates at relatively low lateral loads, a large portion of the plate exhibits elastic post buckling behavior. One common method for determining plate deflection is solving the von Kármán equations. In previous studies, the post buckling elastic deflection of the wall plate has been obtained from these equations using the Galerkin method. However, solving the von Kármán equations is highly complex, and no explicit analytical solution has yet been presented. In this study, the performance of five machine learning algorithms, including Linear Regression, Polynomial Regression, Random Forest, Gradient Boosting, and XGBoost, was evaluated for predicting the maximum elastic deflection of semi-supported steel plate shear walls. Subsequently, a mathematical formula was developed for predicting the maximum elastic limit deflection using polynomial regression. The proposed formula, with a mean error of less than 2 percent, provides designers with an efficient tool for quickly estimating the maximum elastic limit deflection of the wall plate without the need to solve complex equations or performing costly numerical modeling.