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Urea-selective catalytic reduction (SCR) after-treatment systems are used for reducing oxides of nitrogen (NOx) emissions in medium and heavy duty diesel vehicles. This paper addresses control-oriented modeling, starting from first-principles, of SCR after-treatment systems. Appropriate simplifications are made to yield governing equations of the Urea-SCR. The resulting nonlinear partial differential equations (PDEs) are discretized and linearized to yield a family of linear finite-dimensional state-space models of the SCR at different operating points. It is further shown that this family of models can be reduced to three operating regions. Within each region, parametric dependencies of the system on physical mechanisms are derived. Further model reduction is shown to be possible in each of the three regions resulting in a second-order linear model with sufficient accuracy.