Tips on mounting a 31X10.5 tire on a 15x10 wheel... include:
1. Get a mechanic to do it.
2. Be ready to pay extra, because they will be a real pain in the ***.
3. Be prepared for you mechanic's disdain. He wont like you after doing this.
4. Anticipate looking stupid. The tires will look funny.

Ok, on a serious note. These will be a pita to mount, but it can be done.
It will also be hard to balance, especially with an offroad tire, which usually need a lot of weight to balance anyways. If your having trouble try a tube, then remove it and leave the bead on the bottom

It cost me 10 bucks more than usual, and I payed a little on top off that because it was alot more work. But it is doable. It will just look a little.... different.

 

I've seated many tires like that.. ether and a match will set the bead quick like. Or just use a cheeta (high pressure holding tank with larg ball valve. you shoot 100+ PSI into the void and it sets the bead. I use the cheeta on semi tires. if it works on those it will set a extra wide tire and rim configuration.

 

Take the valve core out, and jam a regular shop 3/8" hose onto the valve stem, then as MetalgearMurder said, a huge blast from the Cheedah, I'll do them all day long. Try seating a 275/60/20, standard Dodge Ram 1500 tire.

 

Small town... small garage. The mechanic I go to only has two door garage he works out of.
Great prices. How much do you guys pay/charge with the above methods.

 

So what's the hassle with mounting a 10.50 on a 10" wide rim? I'd guess that because you would have to get the bead to sit wider than it would want to naturally? Thanks fellas!

 

A lot wider than it wants to..
I still like my 15x10's...