USA - Korea - Shanghai - USA trip. Shanghai to USA airplane make 1 stop at Korea for 2 hours.

Pat, you will be eligible for the 144 hour free transit in Shanghai if you travel either on USA - Korea - Shanghai - USA trip or on USA - Shanghai - Korea - USA route.

Justin, Thanks for the answer. However my concern is little bit more than this. If those flights to and from Shanghai were direct flight, I would have no problem. Unfortunately the airline I want to take is Korean Air and it stops at airport in Korea for either ways for Shanghai. Since I have to stay in Korea, there is no way to avoid the situation. Even if the ticket shows flights to/from third countries, Korea is an actual stopover place even if it's only a couple hours. Any idea on this issue?

If so, you won’t qualify for the 144 hour free transit in Shanghai anymore. A visa is needed.