In order to prove that the classical variational principles contain one principle that the reflection law is the constitutive relation, Hamilton principle of nonlinear elastodynamics is established by using the variational integral, starting from the basic equations of nonlinear elastodynamics. Then, after involutory transformation is used, Hamilton theory is converted to the constitutive variational principle with Langrange multiplier method and partial substitution method. It testifies that this variational principle reflects the constitutive relation. Taking the nonlinear material as an example, a new way to obtain the material constitutive relation is provided in this paper, which provides theoretical basis for numeral modeling. It supplements and improves the reflections of three basic rules in the classical constitutive relation:the reflection law of minimum potential energy principle is the balanced relation, the reflection law of the minimum complimentary energy principle is continuous relation, and the reflection law of constitutive variational principle is constitutive relation.