A method of assembling a flip chip IC package includes applying core underfill material to a surface of a package substrate in a pattern including an area corresponding to a core region of an IC die thereon that is to be attached, that excludes of an area corresponding to corners of the IC die. The IC die is bonded to the package substrate by pushing the IC die with a sufficient force for the core underfill material is displaced laterally by the bumps so that the bumps contact the land pads. After the pushing the corners of the IC die are not on the core underfill. Edge underfilling includes dispensing a second underfill material that is curable liquid to fill an area under the corners of the IC die. The second underfill material is cured resulting in it having a higher fracture strength as compared to the core underfill.