Recently I had to replace the hard disk in my Asus Zenbook UX31A. The hard disk though is not a conventional hard disk, but a solid state drive, and replacing it proved to be not trivial. Unfortunately, the SSD in this notebook is an ADATA XM11 model that has a non-standard unique form factor. It is similar to standard M.2, but is not quite it, and no standard SSD will fit in place of it. Fortunately, there is a way around this.
1. Get an adapter that will allow an M.2 SSD to fit in place of the custom ADATA drive. I used this one: http://www.ebay.com/itm/321843326589. There are other options available on Ebay, Amazon or Aliexpress. Look for M.2 adapter for UX31A.
2. Get a replacement SSD. You will need an SSD with M.2 form factor, 2280 size (meaning, 22 by 80 mm) and SATA interface. Be careful: M.2 SSDs come in a variety of sizes, you will need 2280; no other size will fit. I used Trascend model TS512GMTS800.
3. You will need T5 Torx (6-point star-shaped) screwdriver and another Phillips (cross-shaped) PH000 one.
4. Before replacing the SSD you may want to take an image of it and then copy it to the new SSD. There are plenty of options for this. I used Acronis True Image. By the way, to make an image you will probably need to boot the notebook from an exernal drive. I have another post about that here.
5. Turn the notebook bottom up and unscrew 10 Torx screws that hold the bottom lid. Carefully pry the bottom lid open.
6. Here is how the innards of the notebook look. The SSD is in the middle:
7. There is a screw on the ride side of the SSD board, covered by a paper band that says something like "Warranty void if seal broken ore removed". Carefully peel it off (which, unfortunately, voids your warranty) and remove the screw.
8. Carefully slip the SSD board to the right and take it out.
9. Insert your new SSD into the adapter. Line it up carefully, note that it won't fit if you try to push it the wrong side up.
10. Insert the adapter into the slot where your original SSD used to be. Note that the SSD connects to the adapter at a slight angle, so the board's right side will stick slightly out. Very gently press it down (very gently; if you need to apply more than a gentle pressure, something is wrong) and it will line up perfectly with the socket of the screw you removed at step 7. Insert that screw back to fix the SSD in place.
11. There is a porous insulating material glued to the original ADATA SSD (the grey rectangle on the photo above). Carefully peel it off and glue on top of the newly installed SSD. It will protect the board from the contact with the lid.
12. Close the lid and screw the torx screws back. Note that the ones in the middle of the top side (near the hinge) are much longer than the other 8.
13. That's it! The SSD is in place. Now you will likely want to restore the image of you original SSD to the new one.
Additional information: this page has a lot of useful tips.