In this study, constitutive relationships are developed/or normal-strength concrete (NSC) and high-strength concrete (HSC) subjected to fire to provide efficient modeling and specify the fire-performance criteria for concrete structures exposed to fire. They are developed for unconfined NSC and HSC specimens that include compressive and tensile strengths, compressive elastic modulus, and compressive and tensile stress-strain relationships at elevated temperatures. The proposed relationships at elevated temperatures are compared with the experimental results and previous existing relationships revealing several advantages and disadvantages of present stress-strain relationships. These results are used to establish more accurate and general compressive and tensile stress-strain relationships. Further experimental results for tension and the other main parameters at elevated temperatures are needed to establish well-founded models and improve the proposed constitutive relationships, which are general and rational and fit well with the experimental results. Copyright © 2011, American Concrete Intitute. All rights reserved.