>> I have a small device that has a small motor moving a small
>> mechanical structure. The device is very noisy when running,
>> is there any way to shield the box so that the noise will be
>> greatly reduced ?


What Jinx says. Plus:

You need to identify the source of the noise and the noise 
transmission mechanism. eg is the motor per se noisy, is the structure 
acting as a noise transducer, is the noise coupled through the 
mountings etc

It may be that mounting the unit on a "spongy" mount may assist 
greatly. Try some foam rubber of various stiffnesses and thicknesses. 
Not so stiff or so flexible that there is little damping. Critical 
damping is usually ideal - the system will stop in about a cycle if 
power is removed. Somewhat compliant rubber feet can make a vast 
difference to some devices.

Acoustic insulation should be possible. This can again be foam of 
various sorts or something a little 'cleverer' with eg acoustic 
chambers with damping material coupled by holes to a box containing 
the noise source. A whole science in itself. Used in room dividers, 
acoustic tiles. vehicle mufflers and more.

Lead has been mentioned. May in fact work BUT is probably too dense as 
is. People make spun lead fabrics which have excellent sound absorbent 
properties.

A little more information would help people to help you.


        RM


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