Abstract: The flow stress σ, strain rate ε, temperature T and grain size ds are four most important parameters of the hot working. A general physical relationship (eq. 4) among above four parameters during the steady dynamic recrystalization is established according to the dislocation theory, energy conversation low and dimension consistency. It is applicable to both the general hot deformation and the superplastic deformation and make up some common experiment equations into a theory unity. In eq. 4, K is a material constant, Q_G is active energy of grain growing up, R is gas constant. The plastic flow equation (eq. 9) is further analogized, where Q_σ is active energy of plastic flow,K_σσ is a constant, mis sensitivity factor of stain rate. Finally the flow equation (eq. 13) of welding metal during quasi-steady stage of friction welding is set up by measuring the process parameters, such as, friction torque M, temperature T at friction face, equivalent strain rate ε_e of weld metal. The results show that the sensitivity factor of stain rate is great than 0.5, that is, the weld metal is in the superplasticity during quasi-steady stage of friction welding. The mechanical model of the weld metal deformation is verified. The above results are the theory basis of friction welding research and simulate.