For damage localization using GUW, the propagation velocity of the relevant wave is usually a necessary input variable. However, the propagation velocity of GUW is sensitive to applied loads or stresses. An experimental method is used to investigate how the manufacturing-induced residual stress state of an FML, which acts as a form of prestress in the material, affects the wave propagation velocity. This method allows the determination of dispersion diagrams over an extensive frequency range. The experimental results show that the method enables reproducible measurements across different specimen geometries. There is also good agreement between the dispersion relations for the fundamental A0- and S0-modes and analytical solutions. The method does not reveal any measurable influence of different residual stress states set by process modifications on the wave propagation velocity of the two fundamental modes in the frequency range investigated. Additional measurements under externally applied tensile prestress on the test specimens show that a prestress influence on the phase velocity also exists in FMLs. The known influence of a prestress on the wave propagation velocity demonstrates that the influence of the different residual stress states is in the same order of magnitude of the measurement reproducibility when using two different test specimens.