Can I fly to Shenyang Airport from USA, and then can I take a bus or train to Anshan?

Where will you leave from exactly? Anyway, generally from the US to the city, you need transfer at Beijing or other city.

Upon arrival at the airport, you can take the shuttle bus to the city center first. Then a taxi can take you to the local railway station or north railway station, where you can easily catch a train to Anshan.

Thanks, Nick. You're right, I usually do fly into Beijing or Shanghai first; Beijing if the flight goes through New York or Shanghai/ Pudong if the flight goes through Los Angeles. To go through L.A. always seems crazy to me because I live in South Carolina; Seems like I should go through N.Y. But I wanted to fly straight to SY
this time and go from there to Anshan. I don't think I can fly from Beijing to Anshan, can I? Anyway, that's why I was asking about train or bus service to Anshan from SY(SHE).
Thanks,
Ray