Abstract: Analogous to the concept of momentum moment in dynamics, the concept of generalized momentum moment is presented in symplectic system of elasticity. The uniform definitions of generalized momentum and generalized momentum moment are given in symplectic system, which includes rectangular coordinate symplectic system and polar coordinate symplectic system. Some theorems corresponding to generalized momentum moment are studied. The theorem of generalized momentum moment is deduced from Hamilton’s dual equations. The conservation law of generalized momentum moment is obtained, and the conservation condition is given. The physic meaning of the theorem is analyzed. The theorem is verified with some classic problems of elasticity. The theory in symplectic system of elasticity is enriched farther. Consequently, a theory system is formed which is similar to three basic theorems in dynamics. The system consists of three theorems corresponding to three physical quantities, i.e. generalized momentum, generalized momentum moment and Hamiltonian function.