Aims: A magneto-hydrostatic model is constructed with spectropolarimetric properties close to those of solar photospheric magnetic bright points. Methods: Results of solar radiative magneto-convection simulations are used to produce the spatial structure of the vertical component of the magnetic field. The horizontal component of magnetic field is reconstructed using the self-similarity condition, while the magneto-hydrostatic equilibrium condition is applied to the standard photospheric model with the magnetic field embedded. Partial ionisation processes are found to be necessary for reconstructing the correct temperature structure of the model. Results: The structures obtained are in good agreement with observational data. By combining the realistic structure of the magnetic field with the temperature structure of the quiet solar photosphere, the continuum formation level above the equipartition layer can be found. Preliminary results are shown of wave propagation through this magnetic structure. The observational consequences of the oscillations are examined in continuum intensity and in the Fe I 6302 Å magnetically sensitive line.