I will arrive in Beijing on saturday. Can I see a flight that will take me to shenyang the same day?

If you arrive at BJ not very late, you can surely take a direct flight to there, for the schedule is very dense. The travel time is about 1.5 hours, while the cost is not sure. The price varies widely in travel seasons, airlines and seat classes. You can search for the ticket online to get the detailed price. 2 hours is needed between these two flights.