The spatial structuring of solar and space plasmas is known to have a dispersive effect on waves. Many solar features possess a periodic structure with structures having alternating properties. Here the effect of periodic alternation of magnetic slabs on wave propagation is studied when the equilibrium has a steady motion (in line with observations). The dispersion relation for linear compressional waves is derived and analysed. The propagation of waves is studied, in particular modelling the cases of propagation in penumbral filamentary structures in the photosphere, the plume/interplume region and spaghetti structures in the solar wind. Depending on the width of structures (or the wavelength of oscillations) waves have different behaviour. It is shown that the strength of the equilibrium flow has a strong influence on the propagation speed and character of the wave.