Indeed. Compressed nerves and blood vessels can cause this. I came close to getting carpal tunnel once, and believe me, even that was no fun. Odd as it may seem, do exercises before getting on the computer for any length of time. IANAD, but what was recommended to me (by a chiropracter) was to assume a folded hands position, like praying, then extend the arms out until your hands are approximately at a 90 degree angle. Apply light pressure for 10 seconds or so. Then place your elbow on a hard, flat surface (table will do), and bend your wrist down until it's parallel with the table. Apply light pressure for about 10 seconds. Repeat with the other arm. Then put your arm straight out in front you, and bend your wrist until it's pointing straight down. Again, apply light pressure for 10 seconds or so. Repeat for the other arm.
Again, I'm no expert. This was just what a chiro told me to do. The most important thing is light pressure. Don't want to strain something.