Timm's BMW E31 Radio and MID Removal
 

The MID is held in with clips at the top and the bottom edges - it could possibly be forced out, but removing the radio makes it a lot easier. The standard head-unit is held on by two (very long) Allen bolts, accessed under two flaps:

If you have a Becker unit, you will need the special tools:

Remove the radio and place it on the centre console (use a cloth to protect the surface). Use a plastic tool under the MID to unclip the unit and tilt the unit slightly upwards:

Do the same at the top and the MID can be released from the centre console:

When replacing, start with the radio as this allows the radio loom to be adjusted so it does not get trapped behind the radio (especially important if the Becker or other after-market unit is fitted).

All done, time for a cup of tea.