Abstract: In Part One the variational problem is used to describe the generalized variational principles of elasticity. A match problem between the varational constraint conditions, the general constraint conditions and the variational conditions is discussed based on the potential energy density and the complementary energy density.New generalized variational principles are established with lagrange multiplier method based on new potential and complentary energy density. The variational principles opened up a new way for solving the structure engineering problem and set the foundation for establishing the new discretization method.