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Some group invariant solutions of the two-dimensional elastodynamics problem in linear homogeneous isotropic materials are considered using the group-theoretical method.In the polar coordinate system,three group invariant solutions are constructed by the invariants of the Lie group,which are admitted by the goveing equations for the two-dimensional elastodynamics problem.The graphical figures of the group invariant solutions are presented,and the physical meanings of the group invariant solutions are expounded in some cases.