Currently, no river ice models are available that are free and open source software (FOSS), which can be a hindrance to advancement in the field of modelling river ice processes. This paper introduces a non-proprietary (conditional), open-source option to the scientific and engineering community, the River Ice Model (RIVICE). RIVICE is a one-dimensional, fully-dynamic wave model that mimics key river ice processes such as ice generation, ice transport, ice cover progression (shoving, submergence and juxtapositioning) and ice jam formation, details of which are highlighted in the text. Three ice jam events at Fort McMurray, Alberta, along the Athabasca River, are used as case studies to illustrate the steps of model setup, model calibration and results interpretation. A local sensitivity analysis reveals the varying effects of parameter and boundary conditions on backwater flood levels as a function of the location of ice jam lodgment along the river reach and the location along the ice jam cover. Some limitations of the model and suggestions for future research and model development conclude the paper.