As opposed to the responses of structures subjected to loading conditions which are known precisely as a function of time and can be classified as deterministic, Chapter 2 focuses on loading conditions that are typically nondeterministic. There are a number of physical phenomena that result in nondeterministic where future instantaneous values cannot be determined in a deterministic way. These include earthquakes, wind loads, aircraft landing loads, etc., which have unpredictability of their instantaneous values at future times. As a result of this type of loading, termed, random loading, the major concepts of probability are presented. Included within this broad spectrum of topics are probability distribution and density, mean, variance, standard deviation and distributions as well as combined probabilities. The random nature of the loading conditions presented dictates discussions of correlation functions, spectral densities, and combinations of random processes. The dynamic characteristics of linear systems are also presented. The chapter concludes with discussions of the input–output relations for both stationary and nonstationary random processes.