With the recent upgrades to iTunes 12.2 the shuffle feature we used to know and love is gone. With a bit of digging found several ways to get this to work.
In Songs Mode.
- Choose “Songs” not “Artists”, “Albums”, etc.
- Pick a song and start playing.
- Hit the title of the song near the bottom.
- In the new screen, hit the Shuffle button.
In Playlist Mode.
Create a Playlist of your favorite songs and use the same selection method as done with Songs.
Hope this helps a bit. More to come on other Modes and getting shuffle to work as it used to.