Preheat oven to 375 degrees F (190 degrees C). Grease and flour a 9x13 inch baking pan.
In a large bowl, mix together the butter, flour, sugar, baking powder and salt. Beat in the eggs one at a time, then stir in the milk and vanilla until blended.
Pour the batter into the prepared pan.
Bake for 25 to 30 minutes in the preheated oven, or until a toothpick inserted into the center of the cake comes out clean. Serve warm.