Uncertainties can be modeled as random variables or stochastic processes when there is a sufficient amount of data to form a sample space. Random uncertainties may arise from external excitations to the system, or from system parameters. Structural and mechanical systems can subject to earthquakes, ocean waves, wind loading and aerodynamic forces of fast moving vehicles, and from randomness of material parameters such as inaccurate modulus, internal material damping and geometrical variations due to variabilities of manufacturing processes.