It will work fine, there are several designs of tumbler bins that never come in contact with soil. Some people like to be on the soil, so that worms and other critters can participate in the soil making process.

You will likely stain your concrete though. I would see if there is some sort of plastic tray to put underneath. The advantage to a tray, is that you could scoop off any "compost tea" that drains out (good stuff!!!).

Good Luck!
Will

Ya- should work out fine, aside from the stain mentioned by walkindarkroom above. Worms will even find their way in eventually, or you can seed the pile with worms after it cools down. Good thing that people report about composting on concrete- you can scoop it up efficiently with a flat shovel. On the ground you're always chasing it around and scooping up rocks etc too.

All 5 of my pallet bins are on concrete and it works great. I never have a problem with roots growing up from the bottom or weeds and grass growing in from the edges that some people have to fight. However, there is a big crack right down the middle (pre-existing). That is how the worms get in and out at will. As for the staining, as soon as you remove the compost, the sun and rain will bleach it back to normal in short order.