Pressure on the nerves in the wrist and hand from gripping too long and too hard on the handlebars is a common problem in bicyclists.

Take a tip from the professionals like Lance Armstrong. Use biker's gloves and padded handlebars. Both these items are available commercially at your local sporting goods or bicycle store.

Glove material is designed to absorb shock. You can do your part too by consciously avoiding a death grip on the handlebars. Take frequent breaks by opening and closing first one then the other hand.

Keep your shoulders away from your ears. Remember to breathe. This can reduce tension in the entire upper body.