Preheat oven to 375 degrees F (190 degrees C). Grease and flour a 9x13 inch pan.
In a large bowl, sift together the flour, sugar, baking powder, baking soda and salt. Make a well in the center and add shortening, eggs, vanilla and bananas. Beat 2 minutes at medium speed with electric mixer. Pour batter into prepared pan.
Bake in the preheated oven for 25 to 30 minutes, or until a toothpick inserted into the center of the cake comes out clean. Allow to cool.