Continuous efforts to identify and better understand the uncertainties have changed many model parameters and physical phenomena employed in the phenomenological transient models or related computer codes to be estimated by more detailed models. Since their true forms are often not known, however, different modeling assumptions have resulted in various forms of model elements even for a given phenomenon, allowing for different results in the code predictions. In a situation in which there are no rigorous ways to decide the credibility of a specific model element over another, these different model elements can become additional contributors to an overall uncertainty of the physical model predictions. In recent times, most uncertainty analyses of physical models have been focused on the model parameters, without considering the impact of these different model elements. Such levels of uncertainty analysis can only explore a subspace of the true uncertainty space of physical models, and thus the resultant uncertainty tends to underestimate the magnitude of possible uncertainties. Regarding the modeling sources of uncertainty, on the other hand, a model sensitivity analysis has been conventionally utilized to assess the effects of each model element on the code predictions. However, such types of analysis cannot systematically account for synergistic effects of all constituent model elements on the code predictions. A formal procedure is provided for characterizing probabilistically two different sources of uncertainty addressed in the phenomenological transient models (i.e., parametric and modeling sources) and their statistical propagation to obtain the overall uncertainties in the physical model predictions.