In metal forming processes, the evolution of material properties near frictional interfaces drastically differs from that in the bulk. Therefore, it is unlikely that constitutive equations based on conventional tests can adequately describe the material’s response in a narrow layer near such interfaces. On the other hand, it is difficult or even impossible to experimentally measure material properties under conditions that appear near frictional interfaces. An approach based on the strain rate intensity factor is proposed to overcome the difficulty with formulating conventional constitutive equations for the material deforming near frictional interfaces. The strain rate intensity factor is a coefficient of the leading singular term in a series expansion of the equivalent strain rate near maximum friction surfaces. It controls the magnitude of the equivalent strain rate in a narrow layer near such surfaces. Conventional constitutive equations usually involve the equivalent strain rate. The new approach uses the strain rate intensity factor in constitutive equations. Therefore, it is conceptually similar to the approach in fracture mechanics, which uses the stress intensity factor instead of stress components to predict cracks' propagation. Applying this new approach requires a special experimental program, which is discussed, and some preliminary experimental results are presented. Particular constitutive equations of the new type are proposed for an aluminum alloy.