This book presents a comprehensive overview of the formulations and methods for solving a wide range of problems in aero-hydroelasticity, specifically as they pertain to various types of aircraft and underwater vehicles. The research is grounded in modern computational mathematical modeling techniques, alongside analytical and numerical methods. It offers a general characterization of the aero-hydroelasticity problem and its components. The dynamics of elastic aircraft motion are discussed, along with practical applications of these models. Additionally, the book explores approaches to address the oscillations of shells containing fluid and the dynamic responses of structural elements to impact forces. This work is intended for researchers, engineers, graduate students, and advanced undergraduates in universities and technical institutes who are engaged in the challenges of aero-hydroelasticity in structural design.