Concrete filled-circular steel tube (CFCST) columns, when externally confined with carbon or glass fiber-reinforced polymers (FRP) sheets and subjected to axial load, exhibit improved strength and ductility compared to unconfined cases. The mechanical properties of the confinement materials are crucial in determining the stress-strain relationship of the confined concrete. This study presents an in-depth analysis of the stress-strain behavior of FRP-confined CFST columns, based on data from 252 specimens. It examines a range of factors, including various infill concrete grades from 14.15 to 140.39 MPa, two types of carbon steel outer tubes with yield strengths (fy) from 226 to 466.5 MPa, and two types of FRP (CFRP and GFRP) with tensile strengths from 1260 to 4900 MPa. The complete axial stress-strain curve is divided into four phases according to a mathematical expression by Wu and Wei (2015): the elastic phase, nonlinear transition phase, linear softening phase, and residual phase. New formulas for ultimate stress, based on confinement stress, were proposed by Hassanin et al. (2023), while the ultimate strain was calculated using the classical formula by Richart et al. Peak stress and strain were determined through statistical linear regression analysis using SPSS software, based on 252 experimental data points and involved using a combined factor of steel contribution (Elsfco) and FRP contribution (Elffco). Eight specimens were specifically used to validate the models through Finite Element Method (FEM) simulations. The accuracy of the predicted analysis results was also assessed by comparing them to existing models. The evaluation showed that the models successfully simulated the complete stress-strain curve of FRP-wrapped CFST columns under axial load, producing satisfactory results. These four models provide reliable results for calculating ultimate stress, ultimate strain, peak stress, peak strain, and the complete stress-strain behavior of these columns.