Mechanical and thermal properties significantly affect many aspects of machining, such as chip formation, cutting forces, cutting temperatures, and surface integrity of machined products. One of the most important mechanical properties is the material flow stress, which is governed by the field variables including the strain, strain rate, and temperature. Due to the presence of high values of these variables in machining, it is important to evaluate the performance of different material models, typically developed at much lower strains, strain rates, and temperatures. The other issue is to identify the effect of the history of these variables that material microvolume experiences while moving through the shear zones and include them in the model. It is demonstrated that such material models may be suitable choices to describe the material flow in simulation of machining, which leads to an extrapolation from the mathematical form of these models. In addition, this paper discuses the importance of history dependency in flow stress and compares the performance of three commonly employed material constitutive models including the nonhistory-dependent Johnson–Cook (J–C) model, the empirical Oxley model, and the history-dependent Maekawa model. It is demonstrated that among the metals with different crystal structures, the flow stress of face-centered cubic (FCC) metals is highly affected by the strain path and is very little sensitive to temperature and strain-rate changes. In addition, the magnitudes of these effects are discussed.