Freeze-up jamming on regulated rivers is an important aspect of cold regions hydropower operations. The timing and nature of freeze-up jamming has a role in reducing effects to winter discharge conveyance. In northern regions with very mild-sloped rivers, skim ice run is of considerable importance to the formation of a thin and stable cover with low hydraulic resistance. This paper presents a detailed review of skim ice run, including quantitative methods for predicting skim ice formation and a description of its behavior during freeze-up jamming. The review is supplemented by site observations from a large northern regulated river which experiences significant skim ice runs during winter. Following this, a treatment of skim ice run during freeze-up jam simulations is presented for a two-dimensional river ice model (Shen, 2010). The treatment includes implementation of empirical equations to establish skim ice run formation thickness, estimate skim ice floe strength as a function of thermal growth, and facilitate ice cover formation under varying discharge and air temperature conditions. Simulations illustrate the role of temporary discharge reductions on both the formation rate and thickness of ice jams formed mainly by skim ice runs. Further, these simulations highlight that profiles of ice jams formed under cold conditions show smaller final thicknesses relative to those formed under warmer conditions, due to the reduced strength of ice floes formed in warm weather. A brief sensitivity analysis evaluates the cumulative effect of concurrent changes to air temperature and discharge, as well as the impact of varying channel characteristics (i.e., sinuosity and bed slope). Enhancing capabilities of the model to simulate freeze-up jams creates potential for industrial applications, where anticipating the effects of discharge and air temperature on ice jam formation is often of paramount importance for river ice management.