A method for forming a flip chip package by using cone-shaped solder bumps and a package formed by such method are disclosed. In the method, an integrated circuit chip is first provided with a plurality of cone-shaped solder bumps formed on a plurality of bond pads. The cone-shaped solder bumps are equipped with sharp-pointed tip portions such that they penetrate an electrically insulating material layer that is positioned between the solder bumps on the IC chip and a substrate to be bonded thereto. When a lamination process is conducted on the IC chip and the substrate with the electrically insulating material layer thereinbetween, electrical communication between the plurality of bond pads and a plurality of conductive elements on the surface of the substrate is established when the cone-shaped solder bumps penetrate the electrically insulating material layer and form ohmic contact with the conductive elements on the substrate. The present invention novel method therefore eliminates many processing steps that are required in a conventional flip chip bonding process and provides an improved method that saves both costs and time.