What size tires will fit 20x8.5 inch rims. The rims will be going on a 1998 Oldsmobile Intrigue?

not only does that make it look loke some stupid hill billy hood car people laugh at it when it crosses railroad tracks bouncing woldly like it has on suspension. It has to rattle your teeth all in your head but why? is there something wrong with a well engineered susspension with tires that help soak up bumps in the road that can actually go over railroad tracks without looking like a joke in a cartoon movie?

Your not going to get a smooth ride from 20 inch rims. You will feel every road irregularity because it will be sent through the chassis rather than being absorbed by the tire sidewalls. You won't have a choice with the tire sidewall being "too thin". The overall height has to remain the same as the stock tires. By trying to go taller, the tires will touch the suspension components and you won't be able to drive the car.

245/35ZR20 is the best size I think

Marc, 20 inch rims on an Intrigue? Wow, that would really be pushing it. However, with some mods it could be done. The proper sized tires on 20x8.5 rims for your Olds would be 245/35-20. http://tinyurl.com/c3235hp I hope you realize how expensive these puppies are going to be. Expect to pay a minimum of $150 a tire even for an entry level quality tire such as the General G-MAX AS-03 or Kumho Ecsta 4X. http://tinyurl.com/cvbxpwk

Ideally you want the same diameter or the next size smaller. Smaller tires perform better in snow. Look in the door jamb for the factory tire size. It should be P225/60/16. That all said the closest smaller tire by a hair is 245/30/20. It's very close but about 3/4" wider but it fits that rim good. It's kind of an oddball size and you will be limited in brands. If you are going to spend all that money because they ain't cheap, make sure your front end is in good shape, good shocks and an alignment.

I'd say either 225/35 or 245/30, they have roughly the same profile just pick whatever width you like.