Exhaust After-Treatment (EAT) systems are necessary for automotive powertrains to meet stringent emission standards. Computational modelling has been applied to aid designing EAT systems. Models with global kinetic mechanisms are often used in practice, but they cannot accurately predict the behaviour of after-treatment devices under a wide range of conditions. In this study, a numerical EAT model with rigorous treatment of the catalytic chemistry is proposed to investigate the impact of the configuration of individual devices in the EAT system; one of the key design decisions. The performance of the proposed model is first critically assessed against experimental and simulation data from the literature before being applied to design a multi-device EAT system for a diesel engine. The target EAT system is composed of a diesel oxidation catalyst (DOC), an ammonia-based selective catalytic reduction (NH3-SCR) device and a diesel particulate filter (DPF). The steady state behaviour of various EAT designs under operating conditions across the engine map are examined. The DOC-DPF-SCR layout is found to be more beneficial than the alternative DOC-SCR-DPF for the specific engine studied. Furthermore, the DPF-front system is more robust with respect to changes in emission regulations. Flux analysis is applied to study the chemical interaction in the SCR and explain the disadvantage of the SCR-front system. In addition, it is demonstrated in the study that future catalyst investigations should consider more realistic feed compositions.