The aim of this paper is to develop new models for the prediction of the ultimate strength, the ultimate strain, as well as the axial stress–strain relationship of square and rectangular concrete columns confined with carbon fiber reinforced polymer (CFRP) wraps. An experimental database covering 360 specimens with an unconfined compressive strength ranging from 11 to 94 MPa was collected from previous studies. In addition, the performance of eight existing strength and strain models was evaluated using the collected data. In this study, new strength–strain model considering the cross-sectional aspect ratio and the shape coefficient as a function of the depth of the rectangular cross-section was proposed using linear regression analysis. The proposed model provides a better correlation and a good fit with the experimental data compared to the other existing models. On the other hand, a new stress–strain relationship describing the axial behavior of square and rectangular columns confined with CFRP wraps was proposed, in which the parameters of confinement, such as the corner radius and the depth of the rectangular section were considered. The proposed relationship was validated with a set of experimental stress–strain curves and compared with four other existing models. The results showed that the proposed relationship provides good accuracy and better predictions over the existing models.