Flow stress is defined as the instantaneous value of stress required to continue plastically deforming the material - to keep the metal flowing. It is the middle value between yield strength and ultimate strength of the metal as a function of strain, which can be expressed: Flow stress is defined as the instantaneous value of stress required to continue plastically deforming the material - to keep the metal flowing. It is the middle value between yield strength and ultimate strength of the metal as a function of strain, which can be expressed: Hence, Flow stress can also be defined as the stress required to sustain plastic deformation at a particular strain.