In this paper, we analyze semi-discrete and fully discrete mixed finite element
methods for linear elastodynamics problems in the symmetric formulation. For
a large class of conforming mixed finite element methods, the error estimates for each
scheme are derived, including the energy norm and L2 norm for stress, and the L2norm for velocity. All the error estimates are robust for the nearly incompressible materials,
in the sense that the constant bound and convergence order are independent
of Lame constant λ. The stress approximation in both norms, as well as the velocity
approximation in L2 norm, are with optimal convergence order. Finally numerical
experiments are provided to confirm the theoretical analysis.