For　general　damped　linear　systems　with　multiple　eigenvalues,　this　study　provides　a　practical　step-by-step　procedure　of　the　high-order　dynamic　response　analysis.　The　method　derived　in　this　study　has　clear　physical　concepts　and　is　easily　to　be　understood　and　mastered　by　engineering　designers.　Moreover,　a　numerical　example　is　used　to　analyze　the　correctness　and　the　effectiveness　of　the　new　method　by　comparing　the　calculation　results　with　the　theory　solution.