Are you making a big deal of their eating? Are they getting to see a "song and dance" when it comes to meal times? Are they getting extra attention because they can control something that you can't?
I would take away all the emotion out of it. Very matter-of-factly place the food in front of them. If they don't eat it after a few minutes, let them be excused from the table. Make it seem absolutely normal and just fine with you. No emotion.
If they ask for a snack, just say that we will eat lunch in ____ hours or minutes. If they cry, just say I am sorry you are sad, but we will be eating in ____ hours or minutes. No emotion - just in a very matter-of-fact tone.
If they don't like something that you have prepared, just ask them calmly to try it. If they don't like it, then say that they can have the ____ (whatever else is on the table). If they say they are not hungry, then act like that is normal and say,"OK. Maybe you will be hungry in the morning."
The trick is to act like this is totally normal. It's hard at first, but you will get the hang of it. Kids will not starve themselves but they will try every trick in the book to gain control if they are the strong-willed type.