This paper deals with the theoretical aspects concerning linear elastodynamic of damped continuum medium in the frequency domain. Eigenvalue analysis and frequency response function are studied. The methods discussed here use a dynamic substructuring approach. The first method is based on a mixed variational formulation in which Lagrange multipliers are introduced to impose the linear constraints on the coupling interfaces. A modal reduction of each substructure is obtained using its free interface modes. A practical construction of a unique solution is carried out using the Singular Value Decomposition (SVD) related only to the frequency independent Lagrange multiplier terms. The second method is similar to the first one replacing the free interface modes by the fixedinterface modes and elastostatic operator on the interface of each substructure.