Why are some NFL players wearing elastic bands (in pairs) above their
elbows? Only players wearing short sleeved jerseys are doing this, and
not all are.The bands are about 2 wide, and are either white or
black,and not all players are wearing them. Just some.

As you haven't provided a link to a photo...I will take a stab at this.
Nike is now producing 'Bicep Bands' marketed to Football Players
(check it out under equipment on the Nike.com site under football,
can't provide direct link as it is a flash site) Basically they are
sweat bands designed for your biceps so you can show of your work in
the gym (or your 'roid intake, either way.)...
Is this what you are talking about?

If they are more 'elastic' like...I would imagine they would be
supports to help players prevent torn bicep muscles (how would you
know that the long sleeve players are not wearing them?).

If you have a photo you can direct to I will look into it more!

I've seen the bands on most NFL players (no, I didn't count them) and
many college players.  I came to this web page because I asked the
same question.  I remember when athletes started wearing the nose
bands to help open up their nasal passages.  I have a feeling this has
some helpful effact on stamina or performance.