In this paper, the boundary element method (BEM) is used to model mufflers with a built-in catalytic converter (CC) or diesel particulate filter (DPF). The CC or DPF may be modeled as a homogeneous block of bulk-reacting material for simplicity, or by a so-called "element-toelement" four-pole matrix connection in the multi-domain (or substructuring) BEM. The bulkreacting material properties or the four-pole parameters of the CC or DPF can be measured by the two-source method. To avoid cutting a smaller test sample from the CC or DPF, we perform the four-pole measurement on the entire CC or DPF block. However, the large diameter of the CC or DPF may not justify the 1-D plane-wave theory. To partially alleviate this restriction, we also implement a 3-D inverse BEM to fine-tune the measured 1-D four-pole parameters. The 3- D inverse BEM involves computing the impedance matrices of the two substructures before and after the CC or DPF, and using a standard optimization routine in MATLAB to find the optimal material properties that can produce the same transmission loss (TL) in BEM as the measured TL. In our test cases with different configurations, this approach does produce better BEM predictions than using the direct 1-D four-pole measurement.