OP I wouldnt bother listening to half the people here, I checked all my components were seated properly and screws were all tight and then wrapped the case in a towel, and stuffed some various other clothes around my PC, its a fairly big Lian-Li case, and then rammed it into a hard wheelie suitcase to take on a plane with me.
It arrived in one piece, all fully working.
As Tefal says though, big heatsink/fan would best be removed, I only had an arctic cooler on mine.
Need the dimensions of your rig if you want someone to try and find you a large enough case to be honest OP.
Try charity websites or something, charity shops, TK Maxx, TJ Hughes etc.
**edit - ethel austin have just gone into administration, see if there is one near you, I would imagine they sell suitcases too.