Great progress has been made in study on dynamic behavior of the damaged structures subject to deterministic excitation.The stochastic response analysis of the damaged structures,however,has not yet attracted people’s attention.Taking the damaged elastic beams for example,the analysis procedure for stochastic response of the damaged structures subject to stochastic excitations is investigated in this paper.First,the damage constitutive relations and the corresponding damage evolution equation of one-dimensional elastic structures are briefly discussed.Second,the stochastic dynamic equation with respect to transverse displacement of the damaged elastic beams is deduced.The finite difference method and Newmark method are adopted to solve the stochastic partially-differential equation and corresponding boundary conditions.The stochastic response characteristic,damage evolution law,the effect of noise intensity on damage evolution and the first-passage time of damage are discussed in detail.The present work extends the research field of damaged structures,and the proposed procedure can be generalized to analyze the dynamic behavior of more complex structures,such as damaged plates and shells. Great progress has been made in study on dynamic behavior of the damaged structures subject to deterministic excitation. The stochastic response analysis of the damaged structures, however, has not yet attracted people’s attention .aking the damaged elastic beams for example, the analysis procedure for stochastic response of the damaged structures subject to stochastic excitations is investigated in this paper. First, the damage constitutive relations and the corresponding damage evolution equation of one-dimensional elastic structures are discussed.Second, the stochastic dynamic equation with respect to transverse displacement of the damaged elastic beams are deduced. The finite difference method and Newmark method are adopted to solve the stochastic partially-differential equation and corresponding boundary conditions. stochastic response characteristic, damage evolution law, the effect of noise intensity on damage evolution and the first-passage time of damage are discussed in detai the present work extends the research field of damaged structures, and the proposed procedure can be generalized to analyze the dynamic behavior of more complex structures, such as damaged plates and shells.