To note and proclaim the accuracy and stability of displacement input model and multiple support response spectrum(MSRS) when non-classical damping in bottom element is adopted, this paper involves in two aspects-theoretical derivation and calculation analysis. The difference of time-domain model between classical and non-classical damping in bottom element is discussed. On the basis of time-domain model, the formula of MSRS is given and deduced, and it is verified by a numerical example. The derivation and analysis show that the stiffness-related damping term in bottom element does not appear in the displacement input model, the displacement input model and MSRS do not have problems of non-convergence, and the accuracy and stability of the displacement input mode is verified.