Several constitutive equations have proposed to model the strain rate sensitivity of metals to strain rate. This paper presents a comparative of six equations reported in the open literature. All equations are used to fit the yield stress of three copper materials and one steel material at two different temperatures. A specific cost function and an optimization problem are defined. The authors recommend the use of the Cowper-Symonds equation or a modified-Eyring equation as both of them fit well the experimental data while using only three material constants. A modified flow stress Johnson-Cook equation is then proposed for metallic materials.