It is proposed in this paper to use the specific deformation work considering the correlation between the strain, the strain rate of the cutting material and the cutting temperature as a characteristic of material resistance to cutting in the constitutive law.The dependence of the specific deformation work and the yield stress on the deformation under adiabatic conditions is researched and determined due to its close connection with the deformation temperature. Moreover, the possibility of experimental determination in cutting is examined as well. The maximum value of the yield stress is established for the chip forming area and the accumulation zone on the rake face. The softening of the cutting material under isothermal conditions at a strain localisation is taken into account. In addition, it is described here how the material resistance changes due to the softening in the chip forming area and on the rake face of the cutting edge.