Heat oven to 350 degrees. Grease and flour 3 round cake pans (9 x 1 1/2 inches)
Mix flour, sugar, shortening, milk, baking powder,salt, vanilla and eggs in a large bowl with electric mixer on low speed for 30 seconds, scraping bowl occasionally. Beat on medium speed for 2 minutes, scraping bowl occasionally. Pour batter into pans.
Bake 30-35 minutes, or until golden brown and a toothpick inserted in center comes out clean. Cool 10 minutes, then remove from pans. Poke a number of holes halfway through each layer, using the handle of a wooden spoon. Pour milk into holes; cool completely.