A method is presented for estimating an amount of ammonia stored in a urea-based SCR catalyst based on a dynamic model of the catalyst. The model takes into account chemical and physical properties of the catalyst, such as catalyst volume, the number of available ammonia storage cites, adsorption and desorption dynamics, as well as sulfur poisoning, thermal aging, and different catalyst operating temperatures, and generates the estimate based on a measured or estimated amount of NOx in an exhaust gas mixture upstream of the catalyst, an amount of reductant injected into the catalyst to facilitate NOx reduction, and on a measured value of NOx in an exhaust gas mixture downstream of the catalyst. The estimated ammonia storage amount is then used to control the amount of reductant injected into the catalyst to maintain desired ammonia storage amount such that maximum NOx conversion efficiency coupled with minimum ammonia slip are achieved.