Many engineered structures are exposed to some type of randomly fluctuating dynamic loading (e.g., earthquake, explosion, wind, etc.). Random vibration analysis (RVA) provides a rational and efficient framework for the analysis of structures excited by such stochastic loads. Although research related to RVA has been underway for more than 30 years, it has taken a long time for this research to be implemented in practice. In recent times, RVA is being used more widely in practice for a variety of engineering problems, largely due to the availability of such analysis capability within popular finite element software such as ANSYS, I-DEAS, NASTRAN, STARDYNE, etc. Careful implementation of computational procedures can significantly reduce the cost of RVA. Special techniques are also required for computing statistics of principal stresses and related quantities.