This thesis develops and extends a method for modelling acoustical propagation in unbounded domains. This wave envelope method is ideally suited for inclusion into existing acoustic finite element formulations. Results are presented for test cases which show close agreement between the wave envelope results and analytical results. Basis function interpolation in the wave envelope elements can be varied from order 2 to order 10, allowing for modelling of complicated pressure fields solely with wave envelope elements. The system to be solved consists of three frequency independent matrices, allowing easy generation of frequency response data. For large systems a frequency response calculation can consume considerable CPU time and a modal decomposition procedure using Ritz vectors is presented that can significantly reduce computation times, with minimal loss in accuracy. The use of Ritz vectors was also found to give better results than the full solution from some situations.