Constitutive equation for metal plastic forming reflects the relationships among the parameters of stress, strain and strain rate. The accuracy of constitutive equation is a key factor in the research of material mechanism, finite element simulation accuracy and forming failure. The commonly used establishment methods of constitutive equation are summarized. Those methods include experiment method, theory analysis method, neural network method, regression method and inverse finite element method. The advantages and disadvantages of those methods are discussed, and application scope of those methods is summarized simultaneously.