Preheat oven to 350° F. Grease two 9-inch round pans.
In a large bowl, mix together eggs, sugar, cinnamon and oil.
Peel and slice the apples and add to mixture in bowl, coating as you go to keep apples from turning brown.
Mix together the baking soda and flour and add to the ingredients in the bowl. Mix well (best with a fork) until all of the flour is absorbed by the wet ingredients. Pour mixture into prepared pans.
Bake for 30 minutes, or until top is browned and a toothpick inserted in the center comes out clean. Cool completely on rack before removing from pans.