This text synthesizes information for analyzing random vibrations and structures into one coherent body of knowledge. It takes a practical yet progressive look at two major fields related to random analysis: linear and geometrically nonlinear structures, and the behaviour of random structures under random loads. System harmonics and oscillations, random functions and the theory of random vibration are covered extensively throughout the text, which includes innovative methods for calculating the probability of failure of dynamic systems. Simplified examples demonstrate applications for daily use and present new approaches to failure analysis. The author evaluates the use of random process methods for the stochastic analysis of crack growth in detail, providing a better description of failures resulting from crack propagation. For young engineers, the book touches on finite element programmes such as ANSYS and the probabilistic analysis programme TROBAN, facilitating solutions to more complex problems. It also illustrates how to write a FORTRAN programme to build a numerical procedure suitable for the design needs.