Principles of structural acoustics are utilized in novel ways to cancel the transmission of sound and vibration through multi-element flexible barriers. Configurations analyzed include two and three layered plates with elastic interconnections. The substructures have different wave propagation properties and boundary conditions. Both continuous and periodic discrete elastic coupling methods are examined. This research demonstrates that flexibility and controlled resonant behavior can be used to block vibration and sound transmission, even with low structural damping. The main strategies utilized are structural wave cutoff with multi-element multi-path (MEMP) structures and relative phase changes due to boundary reflections. Examples of acoustic transmission loss through panel barriers are presented, and the potential advantages and possible shortcomings of the approach are evaluated. Practical configurations for layered sound reduction materials include designs allowing multiple substructural plates to produce radiation on a given surface, leading to net cancellations of transmitted sound in certain frequency ranges. Experimental results show vibration transmission reduction for several configurations. The work has particular application to the reduction in vehicle interior noise and addresses the need for good acoustic performance of lighter weight flexible structures.