Has anyone tried the invisible fencing for a hunting beagle?

Utilizing an invisible fence doesn't 100% guarantee Hubert won't continue to escape. Some dogs will take the hit from the collar because what they desire on the other side is more powerful than the punishing effects of the shock. Is your dog neutered? The desire to roam can sometimes be curbed if the dog doesn't have the sexuality driving him.

Getting on the roof is pretty impressive! How much time does he spend in the backyard? I suspect that he's bored and looking for stimulation. You can try to manage the situation by not leaving him alone outside, OR by installing alternative deterrents. Some people bury dig-proof products along the fence line. If he goes over the fence, take a look at installing coyote rollers.
Even if those steps keep him in the yard, his mind will still be going nuts for stimulation. Trick training, food puzzles, and daily walks would certainly help take the edge off. Good luck! (And in the meantime, make sure he's tagged and microchipped!)

Invisible fence is effective, but expensive tool. It should be your last resort, because your beagle simply needs enough exercise, and fence does not address that. It only deals with the side effects. It is understandable that not everyone can provide daily exercise , thus invisible fence might be the right solution to your problem. To those who say it is cruel, I say that being a little tough with your dog beats having it run over by a car. Invisible fence provides solid results, while those who judge it for cruelness fail to provide any alternatively effective solutions.

Your dog needs to be exhausted on a daily basis, given a job to do. If you can't provide that at the moment, invisible fence will keep it contained.

The problem with invisible fences is that they can have unwanted side effects for your dog. I do think invisible fences can be great tools, depending on the individual but from what I've seen this is a pretty divisive issue in the dog training community.

The most common complaints/warnings I've seen about invisible fences are that they can:

1. Cause aggression issues: your dog by feel the "vibration" (basically a shock) at the boundary of the fence and associate it with something/someone nearby like a cat, another dog, child, etc...

2. Be ineffective or counterproductive: Your dog may cross the boundary, feel the shock then be too afraid to come back home.

3. Allow Other Creatures Into Your Yard: Stray dogs, cats or other wildlife can still enter your yard, putting your dog in jeopardy if they're in the yard unintended

For some people invisible fences seem to work great, but I'd be particularly worried about it causing issues with a beagle. I boundary trained my beagle mix to stay in our unfenced yard (sort of) but when she sees a squirrel, cat, etc, there's no stopping her from taking off and chasing it. With an electronic fence I'm almost certain she would end up getting out at some point and I'd worry about the psychological or physical damage it may cause her. If you do decide to try an invisible fence for your beagle, I would make sure you put the time into boundary training him(which can be very time-consuming.) Considering he's already prone to escape and has hunting instincts, an invisible fence may not be your best option.

I personally have never used one (I've also never had a private yard, so I can't say it's been an option). I do have a lot of experience with beagles however. I would worry that a beagle's desire to chase any woodland creature around might be too strong for an invisible fence. Beagles have a very one track mind and I have no doubt that if my beagle encountered an invisible fence while running after a squirrel, he'd run right through the shock and I'd never see him again.

I agree ... seems cruel. Also, for a very determined dog not very safe. He just might go through it once to gain what He wants, but you can bet he's not going to go through again just to get back inside his yard. Also, he's vulnerable to other dogs or critters coming into his space. I think they're, generally speaking, a bad idea!

Works real good so long as the collar has batteries!

seems cruel.