The prediction of structure-borne sound transmission in complex built-up structures is of great importance in aeronautic, marine, automotive and building engineering. This book investigates this issue based on the framework of Statistical Energy Analysis (SEA) with the emphasis on coupled plate structures incorporating periodic ribbed plates. It presents fundamental principles, basics and new developments in theories, numerical analysis and experimental measurements to let the reader have a comprehensive understanding on this problem. The study in this book has shown the existence of a tunneling mechanism for wave propagation in the periodic ribbed plate that can result in large prediction errors with conventional SEA. To tackle on this issue, this book provides a novel method named Advanced Statistical Energy Analysis (ASEA) which can incorporate the effect of tunneling and therefore significantly improve the accuracy of the prediction results.