How can I get rid of moles on my lawn without killing?

How awful for you I know Moles dont like noise? and you could try thorn/bramble twigs down their runs. I had a neighbour once who said using 'Round up' on his garden had moved the moles on!

I can understand why you don't want to kill them, actually it's probably only one or two. They are kinda cute. As drc says they hate noise, what about sticking steel rods/stakes into the lawn, as many as possible then as often as you can, give them a wack with a hammer. did you know that they tend to come up to the surface at about four o'clock.
Another idea, what about finding an old speaker, place it facing down on the lawn and play some Des O'Connor records, like in the add with Russ Abbot.

I found using canes with an empty soft drinks can on top and pushed into each molehill as it occured I managed to drive them into the ditch and never saw them again (I think 5 or 6 did the trick)
ps I like the idea of the des o'connor but you may need 'heavy metal'

I feel sorry fot the Moles having to listen to D o'C should think 1 blast and they would never come back.

Agree - Des O'Connor would have me running for the hills in a heartbeat, never to return...

you can buy SORK bulbs which deter moles, just plant them and they last for 2-5years.
just saw them yesterday in the suttons 2010 catalogue.