Braced excavation is a common practice in underground construction for buildings and tunneling in urban areas. To determine the stability and failure behavior of the surrounding soil around the excavation, ensuring that it does not collapse and maintains safety, this study focuses on investigating the undrained stability of a fully supported 3D rectangular excavation with an embedded wall in anisotropic clay. The analysis is conducted through three-dimensional finite element limit analysis (3D FELA). To model the failure behavior of soils, the anisotropic undrained shear strength (AUS) failure criterion is employed in FELA. The factors influencing excavation failure are categorized into four dimensionless variables: the anisotropic strength ratio (re), the embedded rigid wall ratio (D/H), the aspect ratio (A/B), and the depth ratio (H/B). The solutions of the stability number (N), as well as the failure mechanism of 3D excavations, are derived from both the lower bound (LB) and upper bound (UB) approaches. This paper also introduces a novel machine learning approach for predicting the stability of supported rectangular excavations in anisotropic clays. Moreover, this study investigates the potential of using an advanced machine learning model which is XGBoost technique. The gathered evidence indicates that XGBoost demonstrates remarkable precision in forecasting the stability of supported excavation in anisotropic clays.