Abstract: We considered the theory of Noether’s symmetry and conserved quantity for elastic continuous system. Firstly, basic formulas for the Hamilton action variation of elastic continuous system were derived based on the equivalent and nonequivalent parameters variations. Secondly, we gave the definition of Noether’s symmetry for elastic continuous system and obtained the determinant  condition of Noether’s symmetry： Noether’s identity. Then we obtained the Noether’s conserved quantity resulting from the Noether’s symmetry of the system, and put forward the Noether’s theorem for elastic continuous system. Finally, the example of plane wave propagating in the elastic medium was used to illustrate the application of the results.

Key words: Noether’s symmetry, nonequivalent parameter variation, conserved quantity, elastic continuous system