This paper is structured as follows. The WEM discretisation scheme is presented in Section 2. The propagation equation and the flow impedance boundary condition are implemented into the WEM in Section 3. The methodology is then used to compute the propagation through a flow impedance tube and to educe impedance values in Section 4. The results are compared against the data Liners from the grazing incidence tube (GIT) at the NASA Langley Research Center, published by Jones et al. [11] in Section 5. These data are the most extensive available for such a configuration and have been widely used to benchmark the use of flow impedance boundary conditions in numerical schemes [12–14]. These results are discussed further along with the improved efficiency of the methodology in Section 6, before conclusions are presented in Section 7.