Selective catalytic reduction (SCR) is diesel aftertreatment using a reduction agent to reduce nitrogen oxides. Diesel engine regulations are being tightened; therefore, the diesel aftertreatment system should be operated efficiently. In the urea-SCR system, there is a possibility of various faults, e.g., catalyst deactivation by sulfur or hydrothermal aging and fault in urea injection system. These faults interfere with normal system operation and result in increase of NOx concentration at the tailpipe. To prevent this situation, it is necessary to detect system faults. In this study, a first-principle model for SCR system is presented based on mass and energy balance equations. Using the onedimensional urea-SCR model, this research introduces a model-based fault detecting strategy for SCR system. The residuals are calculated as the difference between the model calculation and the actual catalyst system measurement with the system faults. The results of this research are used in fault diagnosis and fault tolerant control studies to meet diesel vehicle nitrogen oxide regulations even in the presence of catalyst faults.