Preheat oven to 350 degrees F (175 degrees C). Grease and rice flour two 8 or 9 inch round cake pans.
Mix the white rice flour, tapioca flour, salt, baking soda, baking powder and xanthan gum together and set aside.
Mix the eggs, sugar, and mayonnaise until fluffy. Add the flour mixture, milk and vanilla and mix well. Spread batter into the prepared pans.
Bake at 350 degrees F (175 degrees C) for 25 minutes. Cakes are done when they spring back when lightly touched or when a toothpick inserted near the center comes out clean. Let cool completely then frost, if desired.