The interaction of the Milky Way (MW) satellite galaxies with the Galactic environment produces tidal tails that are observed as denser concentrations in the sky (e.g. like in the case of the Magellanic Clouds tails or the Sagittarius Dwarf stream). I address via numerical simulations the distribution of Dark Matter (DM) and baryonic tidal streams in the Milky Way environment. Initial conditions (ICs) are modeled after Aquarius A2-to-F2 simulations and after previous literature, employing satellite models made both of baryons and DM. At the end of the simulations, most of the baryons are found still inside their progenitors, while most of DM is easily stripped and redistributed in the MW. Also, stripped baryonic debris ends mostly in the inner regions of the MW halo and it is flatter than the DM debris. A look at the angular distribution of the debris shows that this is oriented at specific angles with respect to the galactic disk. This is found also after rotating the satellites ICs of 90 degrees and running the simulations again. The next step into this investigation will be to extract ICs from latest cosmological simulations and to switch on gasdynamics and feedback to study the impact of baryonic physics on the distribution of satellite debris in the MW environment.