The present research addresses a significant gap in the current literature by overcoming the limitations associated with small, noisy datasets commonly used to predict the axial load-carrying capacity (ALC) of fiber-reinforced polymer (FRP)-encased concrete-filled steel tube compression examples (FCFST). Specifically, the authors present a refined, large-scale database that facilitates the evaluation of the prediction accuracies of three modeling techniques: finite element modeling (FEM), analytical modeling, and artificial neural networks (ANN). This comprehensive comparative analysis, underpinned by a robust experimental dataset, not only enhances predictive accuracy but also provides valuable engineering insights. Unlike previous studies, which often lack data refinement or fail to compare multiple modeling approaches, our work offers a more rigorous and holistic evaluation. The current study aims to recommend and compare the estimates of FEM, analytical model, and ANN model for capturing the ALC of FCFST examples. A database comprising 335 FCFST columns was constructed from previous studies to propose FEM and ANN models while the analytical model was proposed based on a database of 698 samples and encasing mechanics of steel tube and FRP wraps. The concrete damage plastic model was used for concrete along with bilinear and linear elastic models for steel tubes and FRP wraps, respectively. Analytical and ANN models effectively considered the lateral encasing mechanism of FCFST columns for accurate predictions. The FEM exhibited high accuracy with statistical parameters: MAE = 223.76, MAPE = 285.32, R² = 0.943, RMSE = 210.43, and a20-index = 0.83. In contrast, the ANN model outperformed, with MAE = 195, MAPE = 229.67, R² = 0.981, RMSE = 174, and a20-index = 0.89. The R² values between the models indicated strong correlations: FEM vs. analytical (0.876), analytical vs. ANN (0.914), and ANN vs. FEM (0.945), with the ANN model showing the best accuracy.