In springtime it is almost dangerous to walk across our lawn because of all the mole tunnels. It is actually difficult to walk due to sinking into the tunnels with almost every step.
I have not used chemicals on the lawn which results in having a lot of earthworms (earthworms are said to be super sensitive to salts, thus avoid such areas). Moles are reputed to be after grubs of beetles such as Japanese beetles, but the scientific community says they eat mostly earthworms and an occasional grub.
Once the weather is hot and drier, the worms go deeper and the moles follow them, but we are still frustrated by the great amount of damage from their work.
I have read several ways to get rid of them, and some are rather bizarre, it is a matter of 'buyer beware'! It is better explained here in this article, a two page information sheet from Purdue University titled: "Mole Control - Buyer Beware" by Timothy J. Gibb, Turfgrass IPM Specialist, in which he lists several popular deterrents that do not work. Some are frequently seen listed for sale in magazines and catalogs. Others are just old wives' tales, grass roots wisdom, word of mouth hearsay, or whatever you want to call it, that get passed around from person to person that are believed to be true, but are actually fallacies.
The best information I have found is the Purdue University Cooperative Extension Service's publication, Moles by Judy Loven. If the link does not work for you let me know, and I will see what I can do to help. They have changed the URL for that article at least once before, but I tracked it down. I could probably do it again for you if needed. The article covers about all you would ever need to know about moles.
We have had animals trapped, then released in other areas, but moles are a much greater challenge. They are extremely difficult to catch in any method humane or not. Husband/Best Friend/Chief Photographer thought he would take care of the problem here and proceeded to use a trap. He lasted about two days then gave up. If your lawn is completely riddled by them as ours is, and you want to know the challenge you are up against, you might be interested to see an illustration of a mole's kingdom. This link will take you to a map of the mole's world.
Hope you have better luck than I have. I still haven't been able to rid this place of moles. (I bet the fox could have.) They continue to come into my garden from the adjoining properties that were formerly farmland. Maybe someday they will be under control, but I don't think it will happen in my lifetime.
Times I wish it were all fenced and I could have a terrier. I know... terriers and gardening don't mix! ---Neither do gardening and moles.