Among the effects of strain hardening, strain-rate hardening, and temperature softening, it has long been argued about which effect is predominant in governing the material flow stress in machining. This paper compares four material constitutive models commonly employed, including Johnson-Cook’s model, Oxley’s model, Zerilli-Armstrong’s model, and Maekawa et al.’s model. A new quantitative sensitivity analysis of the material flow stress is performed based on Johnson-Cook’s model covering a wide range of engineering materials, including plain carbon steels with different carbon contents, alloyed steels, aluminum alloys with different chemical compositions and heat treatment conditions, copper and copper alloys, iron, nickel, tungsten alloys, etc. It is demonstrated that the first predominant factor governing the material flow stress is either strain hardening or thermal softening, depending on the specific work material employed and the varying range of temperatures. Strain-rate hardening is the least important factor governing the material flow stress, especially when machining aluminum alloys.