Dissipative silencers are widely used in HVAC ducts to attenuate broad band noise. Modelling typical HVAC configurations is far from straightforward and to date design techniques rely on a simple modal analysis, quantifying the attenuation of the fundamental acoustic mode and possibly the first higher order mode. Whilst this approach will provide some insight into silencer performance it necessarily suppresses the complex multi-modal behaviour present in larger ducts and/or at higher frequencies, and omits the influence of the outlet/inlet planes of the silencer. The research reported here demonstrates a relatively simple, and computationally straightforward, technique for analysing multi-mode sound propagation in a finite section of a dissipative splitter silencer. Theoretical predictions are obtained using both a multi-mode analytic and a finite element method; the computational efficiency of the latter is maximised by meshing only a duct cross-section and employing point collocation to match across discontinuities. Remarkably good agreement between the two techniques is demonstrated, as is the suitability of point collocation for use in an iterative design environment. Moreover validation of the (computationally efficient) finite element scheme provides confidence for the future use of the technique in analysing more complex HVAC systems, including complex dissipative silencer designs, additional silencer sections, and noise breakout/breakin.