Uncertainty quantification is an emergent field in engineering mechanics that makes use of statistical sampling, hypothesis testing and input-output effect analysis to characterize the effect that parametric and non-parametric uncertainty has on physical experiment or numerical simulation output. This publication overviews a project at Los Alamos National Laboratory that aims at developing a methodology for quantifying uncertainty and assessing the total predictability of structural dynamics simulations. The propagation of parametric variability through numerical simulations is discussed. Uncertainty assessment is also a critical component of model validation, where the total error between physical observation and model prediction must be characterized. The purpose of model validation is to assess the extent to which a model is an appropriate representation of reality, given the purpose intended for the numerical simulation and its domain of applicability. The discussion is illustrated with component-level and system-level validation experiments that feature the response of nonlinear models to impulse excitation sources. This publication is unclassified; it is approved for unlimited, public release (number LA-UR-01-3828).