There are several tactics you can employ in your battle against moles. First, check to see if you have any white grubs in your lawn. White grubs are a favorite food of moles. By eliminating their food source it is most likely the moles will move on.
You can also try flushing moles out with water. Simply poke a garden hose into a tunnel and turn on the water. Leave running for about 15 minutes. The adults will escape, but if done in the spring, you will eliminate the young.
You can also use buried walls as an effective preventative for moles. Create a stone or compacted clay wall around the area you want to protect. The walls should be at least 6 inches thick and extend into the ground 2 feet. Note that this will not prevent a mole from entering the area by climbing over the barrier.
There are several non-lethal traps and repellents on the market that also help in mole control.