2001 Hyundai Elantra: thumping

My Elantra has been running great up until now. It has about 80,000 miles. Recently I began hearing a thumping noise that sounds like either a flat or something caught in the tire. But there is no visible problem with the tires. It only happens when the car is in motion, and the rate of the thump increases with the speed of the car. Then it goes away as quickly as it came. Any ideas on the cause and the recommended treatment would be much appreciated.

Have someone look carefully at the tyre tread as you drive away (both front and back) see if there is a little wave in the tread on one of the tyres. If so, then you will know it has a belt that has slipped and needs to be replaced. How many miles on those tyres?

Don’t replace one tyre unless you have very few miles on it and can get the same kind of tyre. Always put the best tyres on the back. Yes I said the back and that includes FWD cars. It is safer that way.

I once had a Nissan Sentra that made a similar sound (clank, clank, clank) and it was the drive shaft that had to be replaced. Could it be the same case on this car?

I did as suggested above, but found nothing. Could a problem with the axle or drive shaft be causing the occasional clunking?

elantras do not have driveshafts.so you are 50% of the way there.

WWWAG! on the issue though.but rest assured ,NO DRIVESHAFT.