What would cause a thumping noise like a flat tire with a little shake in the steering wheel?

More than likely, if the tire is not flat, and the steering wheel shakes, your problem is a bulge in your tire. As someone else has said, it is probably caused by a bad tire. It may have a broken belt. Also, some tires develop flat spots if the car sits too long. Does it happen constantly or just when you start driving? As a last suggestion, I would check that all of your lug nuts are on tight. If a wheel is loose, you might experience sloppy driving - especially going around corners. The problem should be resolved when the wheel falls off. The "bulge" refered to in answer 1, and the "bad tire" in answer 2 is PROBABLY the cause of your problem. However, a "broken belt" very seldom occurs, almost never unless the belt has been "cut" in a severe collision with a sharp edge. Also, answer 2 alludes to what we used to call, many years back, tire "morning sickness," which occured after a nylon belted tire had sat all night on the same part of the tire. The ground contact point of a tire is slightly flattened, and the nylon belts would take a temporary "set," so that until the tire was driven long enough to warm up the tread and nylon belts the temporary flat spot would cause a slight thumping and jarring. I thought that all nylon belted tires had been replaced by steel belted, meaning that issue should be non-existant today. As answer 2 asks and suggests, does it just do it [thump] when you start driving? If so, then it probably is morning sickness, and there is no cure, just live with until it is time to replace the tire(s). Also, you mention a slight shake in the steering wheel, which would suggest that the offending tire is one of your front tires. Even a thumping rear tire can be felt in the steering wheel, BUT you will also feel it more strongly through your seat if it''s on the rear. A thumping front tire can also be felt in your seat, but will feel, relatively, stronger in the steering wheel. The number one cause of bulging spots on radial tires is what is called "belt separation." A tire is made of several layers of belting material laid up like a sandwich, with the layers "glued" together. IF a flaw allows air from within the tire to work it's way into the sandwich, it can cause some of the layers to separate, fill with air, and cause a bulge, or "blister.' Due to the air pressure, this bulge can be very hard, and will cause the tire lift and thumping you describe. Answer 2 also makes a VERY GOOD SAFETY point, in that loose lug nuts on one of the wheels can cause a similar symptom, BUT left on it's own [withour proper retightening], will continue to become looser, until the wheel FALLS OF THE VEHICLE!!!! DO NOT allow this to happen. Periodicaly [spelling?] check the tightness of your lug nuts on all wheels, or have your tire service people do it. It could save your life!!!! Also, check and adjust your tire pressure REGULARLY, weekly at a minimum.