Vibration and noise reduction are important technology to realize comfort products with safe structures. In this paper, we carry out numerical simulation of damped vibration and sound radiation for structures having a porous material sandwiched by double walls. The double walls are consisted of a steel base plate and a steel cover plate. The cover plate in double walls has a Krylov type acoustic black hole. Damping material is on the surface of the black hole. One point in the base plate is excited by white noise. Numerical analysis is performed to clarify changes of vibration transmission from the base plate to the cover plate due to the acoustic black hole using FEM and MSKE method(Modal Strain and Kinetic Energy method) proposed by Yamaguchi et al. Sound radiation from the cover plate is also investigated. The vibration transmission were reduced for the model having acoustic black hole in the cover plate. Vibration energy flows into the black hole in the cover plate. This causes that vibration acceleration of the cover plate is damped effectively. Sound radiation from the cover plate also decreased. This is because high damping and shorter wave length of vibration in the acoustic black hole.