Intensifying flooding around the world can be a threat to human infrastructure, human life, and ecological integrity of river systems. Flash floods can be particularly dangerous for downstream communities, especially in mountainous regions, since flood stages rise quickly and evacuation times are limited. Understanding the mechanisms of flash flood propagation in mountain stream networks is essential for implementing flood management strategies. Standard flood routing methods were typically developed assuming low-gradient river networks with small spatiotemporal variations in discharge or river characteristics. The applicability of these methods has not sufficiently been tested in steep-gradient systems with floods exhibiting short times to peak discharge. Thus, in this study we evaluate the performance of numerous common flood-routing methods on flood propagation in headwater streams. We developed five numerical models that capture different hydraulic or hydrologic processes for three streams located in the Colorado Front Range of the Rocky Mountains. These models included spatially uniform 1D hydrodynamic models, and four variations of Muskingum-Cunge hydrologic routing models. For each model we compared output hydrographs using Kling Gupta Efficiency, Nash Sutcliffe Efficiency, difference in peak flow attenuation, and differences in predicted total volume retained within the models. We found that standard Muskingum-Cunge routing methods are insufficient in reproducing flood hydrographs because they underpredict water retention within the floodplain and overpredict peak outlet discharge. The model that most effectively reproduced flood routing when compared to 2D hydrodynamic models was a new method we developed to account for floodplain storage of water, which we refer to as the Muskingum-Cunge Augmented Floodplain method, and which scales the volume of water retained on the floodplain by the overall inundated floodplain volume. Our results indicate that hydrologic routing algorithms, such as the classic Muskingum-Cunge approach, need to account for mass storage of water in floodplains to accurately predict the attenuation of flash floods in mountain streams, and our Muskingum-Cunge Augmented Floodplain routing scheme improves predictions of flood routing.