Joined: Feb 2013
Posts: 1,472
Likes: 11
From: Near St. Louis, Missouri
Bikes: Giant Defy Advanced, Breezer Doppler Team, Schwinn Twinn Tandem, Windsor Tourist, 1954 JC Higgens
Are you saying that it moves from side-to-side, up-and-down, or both?
The first thing that I'd check would be that the tire is seated properly. Deflate the tire and check that the tube isn't stuck between the tire and rim. Next inflate the tire to about 10 psi and check that the tire is seated about the same way on both sides of the wheel. Then inflate to the pressure that you ride and check where the tire touches the wheel again.
Other problems could be a bent rim or even a defective tire as you rode on it uniflated.