Preheat oven to 350 degrees F (175 degrees C). Bake potatoes in preheated oven for 1 hour.
When potatoes are cool enough, cut them in half. Scoop the potatoes into a large bowl, leaving the shells intact. Mix potato with mayonnaise, tuna and green onions. Spoon mixture back into shells. Press shredded cheese on top of each.
Bake in preheated oven for 20 minutes, or until cheese is melted.