So...have a 96 Buick Park Avenue Ultra that feels like the CV axle is going bad. Symptoms are as follows: under slow speeds turning right at a stop sign the car feels like I have a square wheel or something. Makes a shudder/big vibration or something... Feels like the right side. We thought it was the CV axle but after we jacked it up, AND a mechanic put it on the lift, it shows no play on the axle or the wheel. Once, after we jacked it up and put it back down...the problem disappeared. Just took an 800 mile trip and all was fine till the last 200 miles. Then...at acceleration... Even very slight acceleration... The car would shake violently again, and it appeared to be the front again. But when I'd let off the gas it seemed OK. Just got back from the mechanic, who drove it with me for 15 minutes, and he couldn't diagnose it in the air or on the ground. Happens at different speeds and intermittently as I said. Any help will be appreciated. Someone please help! Thanks in advance.

When is the last time the tires were inspected, and properly balanced?
I had similar issues and it turned out to be that I had gotten a horrible balancing job from Walmarts Tire Lube Express, I'll never go to them again!

New tires 2 years ago. The mechanic actually said it felt like that at first, but ruled it out as this happens at all speeds.

It may not be the tires then, I had some old Viva II Touring tires sold by Walmart, they are discontinued now though.
I am pretty sure the belts had started separating, and the tires were definitely not balanced correctly.

Have you had the balance checked on the tires since this condition started?

Does the vibration transfer up through the steering wheel?
If so the inner tie rods could be going bad, mine had lots of play in them, and were adding to the wobble I had going on.

I'll look over my Factory Service Manual and see if I can find the steps for diagnosing this issue, I had it posted on another site, but I doubt I'll find it as it was posted years ago.

Actually found the post on the other site I am a member of, luckily it is from a site we are allowed to share links from.
This thread has all the info needed to properly diagnose the vibration.

Vibration Diagnosis and Correction - 3800Pro.com Forum

Thank you so much for taking the time to both respond and find the article. I will definitely be taking a look at it tonight. I will also check the wheel balance, and yes you can feel it through the steering wheel.

Tires are not intermittent.....

If front end checks out, I'm leaning towards CV joint....

Normally I'd agree, but the issue I had was not 100% of the time, and new inner tie rods got rid of about half of the vibration, then I had a good bit of vibration at certain speeds till I got new tires, and had them balanced.
Maybe it just seemed intermittent, I guess the vibration could have been so slight at lower speeds that I could not feel it all of the time.

Just keeping everyone updated. Car goes to the mechanic tomorrow morning. I've decided to replace the CV axles, but I'm doing one at a time. They'll replace the drivers side axle tomorrow. I just believe that the axle/axles are the issue, and if I had to guess I would think it is the driver side. One more point...there is not excessive play in the axles when examined, but I believe there is unusual wear that is causing this issue. Hope I'm right.

Good luck!
I'd try to replace both at the same time if possible, that way you save a little time as they can do both while it is on their lift, but if they won't charge much more then I guess you will be fine doing one at a time.