Most of the existing studies conducted on FRP-confined concrete considered circular and square concrete columns, while limited studies were on columns with rectangular sections. The studies have confirmed that the circular cross-sections exhibited higher confinement effectiveness, whereas in the case of non-circular cross-sections the efficiency of FRP confinement decreases with an increase of the sectional aspect ratio and there is no significant increase, particularly for columns with the aspect ratio of 2.0. As recently suggested by the researchers, to significantly increase the effectiveness of FRP-confinement for these columns is by modifying a rectangular section to an elliptical or oval section. According to the literature, most of the existing confinement models for FRP-confined concrete under axial compression have been proposed for columns with circular and rectangular cross-sections. However, modeling the axial strength and strain of concrete confined with FRP in elliptical cross-sections under compression is most limited. Therefore, this paper provides new expressions based on limited experimental data available in the literature. For a sufficient amount of FRP-confinement, the threshold value was proposed to be 0.02. Finally, the accuracy of the proposed model was verified by comparing its predictions with the same test database, together with those from the existing models.