I have done this a lot. Computers in luggage to Costa Rica, UK, and Malta. Mainly to avoid paying incredibly high VAT taxes and uncompetitive prices for local machines. All of the computers were Dell and all of them traveled well with no damage. I used soft sided, canvas luggage like rolling duffel bags.

The best way (for me) to pack the computer is to use the original styrofoam packaging that came with it. I use packing tape to secure the styro to the machine and fill in all other spaces with clothes. Then I put a layers of clothes under and around the machine once it is in the suitcase.

You can use the same procedure for the monitor. I hope you are using a flat screen monitor because a full size one will use an entire suitcase once it is packaged.