Engineers must deal with risks and uncertainties as a part of their professional work and, in particular, uncertainties are inherent to engineering models. Models play a central role in engineering. Models often represent an abstract and idealized version of the mathematical properties of a target. Using models, engineers can investigate and acquire understanding of how an object or phenomenon will perform under specified conditions. This paper defines the different stages of the modeling process in engineering, classifies the various sources of uncertainty that arise in the each stage, and discusses the categories into which these uncertainties fall. The paper then considers the way uncertainty and modeling are approached in science and the criteria for evaluating scientific hypotheses, in order to highlight the very different criteria appropriate for the development of models and the treatment of the inherent uncertainties in engineering. Finally, the paper puts forward nine guidelines for the treatment of uncertainty in engineering modeling.