Elavil does two major things.

Depending on dose, you may see some antidepressant effects.
Typically at low doses used for PN this is not obvious. At 50mg a day and above you may see antidepressant effects. The neurotransmitters in the brain, are involved in the "pain loop" in the brain and some antidepressants work on serotonin receptors there to dull perception of pain.

The second thing Elavil does, and this has been shown more recently in a study, is that Elavil can improve nerve growth factors in the peripheral nervous system. So it is rather unique among the antidepressants in this function. So yes, it can actually improve nerve functions in the periphery.
This latter effect is not going to be found most likely on any informational print out at the pharmacy level. It is too new I would think. You can read more about it here:
http://neurotalk.psychcentral.com/sh...=amitriptyline

Nortriptyline (Elavil's active metabolite) also works this way.