Combine Cheddar cheese and butter in a large mixing bowl; beat until smooth. Add flour, salt, and paprika, stirring well.
Shape dough into 1/2-inch balls; gently press each to 1/4- inch thickness. Place wafers 1 inch apart on lightly greased baking sheets. Bake at 450° for 7 to 8 minutes. Remove wafers immediately from baking sheets, and place on wire racks to cool.