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The ductility and energy absorption characteristics of concrete-filled steel tube columns (CFSTCCs) make these columns a good choice. In this paper, the three-dimensional (3D) nonlinear finite element method (FEM) (3DFEM) modeling, and simplified numerical modeling results, are compared to those of the computation methods presented in previous studies on estimating the ultimate load capacity of circular stub concrete-filled steel tube composite columns (CFSTCCs). Another comparison between practical design methodology approaches based on advanced analyses, namely, multivariate adaptive regression splines (MARS), relevance vector machine (RVM), and artificial neural network (ANN)-based models were also presented by Avci-Karatas. In order to improve the accuracy of the modeling process and achieve more precise predictions, a thorough set of experimental data was collected. This data encompassed the geometrical and mechanical properties of circular CFSTCC, including parameters such as height, diameter, thickness, steel yield stress, unconfined concrete strength, and Young's modulus for steel. In the present study, it is found that the predicted ultimate axial compression load capacity of circular stub CFSTCCs based on 3D-FEM, numerical modeling, and MARS, RVM, and ANN-based modeling is comparable with the experimentally measured values. In the MARS-based model, the minimum and maximum values of the predicted-to-experimental ultimate axial load ratios (PuMARS / PuE) were found to range from 0.87 to 1.10. For the RVM-based model, the ratios (PuRVM/PuE) varied between 0.90 and 1.06. Similarly, in the ANN-based model, the ratios (PuANN / PuE) ranged from 0.92 to 1.04. As powerful statistical modeling tools as MARS- and RVM-based models are, ANN-based models, achieve high computational efficiency in terms of accuracy in the context of this paper. [ABSTRACT FROM AUTHOR]