Steering Wheel shakes

I have a 2006 Hunddai Elantra. I fixed the alignment and the garage rotated tires. The problem I have is that steering wheel shakes at any speed, but the shaking decrease when touch the brake.

You MAY have a bad brake rotor.

When your tires were rotated did they rebalance? I’m guessing you had an alignment due to something shocking the car out of alignment, like hitting a curb, slamming on the brakes or hitting something in the road. I had the problem a few times and both for different reasons and one of them was a slight dent in the wheel from a pothole in the road.
Good luck

when you had the tire rotated did you go back to the shop to get the lug nuts retourked agein? becuse they may not all hve being snug. also you could have a tire that is cupping, form the rear and is making the wheel shake. you can check by running your hand over the tire in both deractions to see it one ways makes resetances on your hand. tire dude

If you had the alignment done because the tires were wearing unevenly - well, that’s good. If true, then you probably also got irregular wear on your tires. Irregular wear is caused by misalignment and aggravated by insufficient inflation pressure and insufficient rotation practices. Irregular wear comes out as a vibration that you either hear or feel (or both).

Fixing the alignment fixes the cause of irregular wear, but the wear pattern is still there. To fix the wear pattern you either have to be patient and wait for the new wear pattern to replace the old one - or - replace the tires.