In this study, we have developed a kinetic model for ammonia-SCR over a well-characterized Cu/SSZ-13 catalyst. It was found that a three-site model was needed in order to describe the ammonia temperature programmed desorption (TPD) with adsorption at 50 and 150 °C as well as ammonia oxidation, and NH₃-SCR up to 600 °C. Based on literature studies, where detailed characterization of Cu/SSZ-13 have been conducted using several experimental techniques, we suggest the following physical interpretation of the S1 and S2 sites in the model. The S1 sites are associated with copper located in a six-membered ring, possibly slightly distorted due to interactions with water and ammonia while, the S2 sites represent copper in the large cages or Cu_xO_y species. In addition, ammonia is also stored on Brönsted acid sites, but in order not to complicate the model further, it was lumped together in the S1 and S2 sites. Finally, S3 sites have been added in order to describe the large amount of physisorbed ammonia at low temperature. This three-site model was capable of adequately describing the ammonia TPD experiments with the initial temperature of 50 and 150 °C. The heats of adsorption of ammonia on the S1 and S2 sites were determined using micro-calorimeter experiments. Further, the main SCR reaction in the model occurs on S1 sites and the main ammonia oxidation reaction on S2 sites. However, due to the complex behavior associated with ammonia oxidation, where the conversion slightly decreased when the temperature was increased from 350 to 400 °C, an ammonia oxidation reaction occurring at low temperature with low rate needed to be introduced on S1. In a similar way, an added step was needed for ammonia-SCR on S2, which occurred at high temperature where the ammonia coverage on S1 was low resulting in low conversion. To summarize, the three-site model developed was capable of well describing the ammonia storage and release, ammonia oxidation as well as SCR and N₂O formation across a broad temperature interval (100–600 °C).