First possibility -- shoot through a hole in a black panel, so no light
is coming from the camera; supply all light from the sides (out of
field, of course), very diffuse (broad source light behind a muslin
sheet, frosted plastic, etc.); that should show up the relief of the
carving with little or no glare from reflections into the lens.
Alternately, one to three point sources to the side, still shooting
through a hole in a black panel, might give less glare if the relief is
high and reflects the diffusers into the lens; instead of broad areas of
glare, it will then be reduced to an array of points.

Either way, be sure to use either enough light or a camera mode that
will turn off any on-camera flash, to avoid direct glare.

I wrote this for another thread in a different USENET forum,
but it seems to apply to your situation.

= = = = =
The first thing is loose the camera's built-in flash and get
some decent lighting equipment. Then see some of the
tutorials that are *free* on the web ... such as

Basic Product Shot
Basic Product Up-Close
Techniques for Jewelry
Fine Tuning a Product Shot
Shooting Product Shots with a Photoflex Litedome
    all at
http://www.webphotoschool.com/bhphotovideo/index.html

Or go to
http://www.webphotoschool.com/newschool/Default.asp
and click on "Free Photo Lessons"

Or go to Adorama's site and read
http://www.adorama.com/catalog.tpl?op=article_080403

Or go to Ganoskin's site and read through their articles on
jewelry photography
(includes tips on how to make the equipment you'll need)
http://www.ganoksin.com/borisat/directory/library/subject/9

Why do you want to? The shine is part of the object.

Why do you think that?

Traditional way is to use crossed polarizers to eliminate all reflection:

 o  one polarizer filter on the camera
 o  one sheet of polarizer on (each of) the light(s)  

 o  Replace the subject with a mirror
 o  Fix the camera polarizer (without camera) to a stand
    with tape so you can look through it;  put a dot of tape etc.
    at the top of the polarizer ring.

 o  Turn the lamps on one at a time and rotate the polarizer
    sheets on each lamp so when looking through the camera
    polarizer (at the lamp reflected in the mirror) the lamp
    light disappears
 o  Mark each sheet of polarizer so adjusted with a dot at the top.
    Fix them to the lamps.

 o  If you have hot lights (i.e. not flash) then you can look through
    the camera polarizer and twiddle the lamp polarizers to add 'just
    the right amount' (ha!) of highlight.

 o  Put polarizer filter on the camera lens and adjust so the dot
    is at the top
 o  Take pictures

Sometimes just using a polarizer on the camera will be enough.

There is a spray just for this purpose called dulling spray - make sure
it is the temporary stuff! - you spray it on and it comes right off again
with a Kleenex.  You may not like the effect.  Available at theatrical supply
houses or large photo stores.

Try the biggest, best and cheapest diffuse source: outside on a
grey day.  Try moving a sheet of white cardboard around to reflect
light up into the dark spots on the sculpture.  This reflection technique
should also be used if you are using the artificial light method, above.

Use a lamp (a friend with a flashlight will do) to create highlights.

Also:

Try a sunny day, put the sculpture in light shade, and move large pieces of
white card, aluminum, etc. around to reflect in a little bit of sunshine.

You may need a circular polarizer, or you may not.  If it is the usual type
of digital camera you may have to use sticky tape to hold the pola filter
to the camera.  If you rotate the camera from horiz to vert you will need to
unstick and restick the filter so the dot on the filter is always up.

Any good camera store can supply the camera filter.  Try theatrical supply
houses for the polarizer sheets for the lamps.