The conversion efficiency, durability and pressure drop of the automotive exhaust catalysts are dependent on the flow distribution within the substrate. Conventional porous medium approaches assuming monolith resistance based on the one-dimensional laminar flow for simulating the flow through the automotive exhaust catalysts over-predict the flow uniformity in the monolith. In this study, additional pressure loss is also considered by accounting for entrance effects due to the oblique flow incident on the front face of monolith as a consequence of flow separation and recirculation within the diffuser. The incorporation of an additional pressure loss improves the predictions for the maximum flow velocity within the substrate. An numerical study has also been conducted for the three-dimensional unsteady incompressible non-reacting flow inside various dual-monolith catalytic converters for the rapid acceleration/deceleration driving.