Structural fire safety capacity of concrete is very complicated because concrete materials have considerable variations. In this paper, constitutive models and relationships for concrete subjected to fire are developed, which are intended to provide efficient modeling and to specific fire-performance criteria of the behavior of concrete structures exposed to fire. They are developed for unconfined concrete specimens that include residual compressive and tensile strengths, compressive elastic modulus, compressive and tensile stress-strain relationships at elevated temperatures. In this paper, the proposed relationships at elevated temperatures are compared with experimental result tests and pervious existing models. It affords to find several advantages and drawbacks of present stress-strain relationships and using these results to establish more accurate and general compressive and tensile stress-strain relationships. Additional experimental test results are needed in tension and the other main parameters at elevated temperatures to establish well-founded models and to improve the proposed relationships. The developed models and relationships are general, rational, and have good agreement with experimental data.