This publication covers applications of the random vibration theory to the analysis and design of a wide range of structural and mechanical systems and operating environments. These include the modelling and simulation of random processes, fatigue in random vibration, design in a random vibration environment and the response of aerospace structures to atmospheric turbulence. Also covered is the response of structures to earthquakes, wind and ocean waves, and statistical energy analysis. The authors concentrate on engineering and design aspects, including the use of approximations to develop practical design problems. They demonstrate that a wide range of problems is amenable to a unified treatment for earthquakes, wind and ocean waves.