I feel your pain. I have the same problem, and I have been trapping for 2 years now. It reduces the damage, but like you said, other squirrels move in over time. So far this year I have relocated 6 of them. Squirrels dig holes to bury nuts, or to dig them up. If you have nut producing trees then you will have more problems then if you didn't. In my case most of the damage is related to 2 large hickory trees on one corner of my property. I have looked into other solutions but the only one I have heard works is a huge endeavor. You have to get a ton of crushed oyster shells and basically create a layer just below the top inch of topsoil. Apparently this is very tough on the squirrels hands and they don't like digging in it (this isn't an April Fools joke by the way). Another thing that might work, but isn't really feasible is applying cayenne pepper to your lawn periodically. The problem is that cayenne pepper is very expensive in those quantities, plus it would probably bother you as well, but maybe if you suspended it in water and applied it with a sprayer it wouldn't be so bad, or expensive.

Thanks Tiemco. Yes, in the yard in back of me is a huge oak tree...I'm sure that's why the squirrels love my yard.
The oyster shell idea sounds great but I wouldnt be able to dig up my beautiful lawn to lay it down. I could try the red pepper....There is a restaurant supply house I know of and perhaps i can get large quantities there....OR I did a little research since my post and someone suggests in their article to be diligent in the trapping and then submerge it in water or to put the trap in a sack or bag and tie it to the end of the car exhaust pipe for a few minutes. Their position is that elimination will keep the population under better control than trapping and relocating.

If I didn't live so close to other people my .22 would be working hard on the squirrels. I don't think drowning is a humane way to dispatch them, and gassing them seems like too much trouble. I don't see the difference between killing and relocating, either way they are removed from the area. I drive a few miles away to an open space area that's across a river. Plus nature has a way of keeping populations in check, except for those damn deer, that's our fault for removing all their predators.

You really cannot eliminate them, just keep them in check. I live in the country and between squirrel eating dogs, .22, and shotgun I can keep the numbers down. But after decades they still keep coming.

scottys, You're constantly filling in little holes in your yard caused by squirrels. So what's the big deal? I have squirrels too but I just ignore them mostly. You cannot eliminate them nor can you control the population on your own. I can't believe anyone would drown them or gas them with exhaust gas. Why not create a little electric chair for them in view of the Oak tree. Perhaps capital punishment will deter other squirrels from entering your yard....On the other hand, why not just enjoy the little critters? Holes in your yard......good grief.

Here is a link that might be useful: {{gwi:85756}}

That electric chair sounds like a great idea. But seriously, it goes way beyond holes in the yard for some people. One area of my fall renovation is, for all intents and purposes, ruined. It's not a neat little hole like an aerator makes, it's like the practice tee on a driving range. I know they are just doing what they are supposed to do, but if I can minimize the damage in a humane way I will continue to do so.