Shear strengths of BGA solder joints on Cu pads were studied for Cu-containing Sn (0, 1.5, and 2.5 wt.% Cu) and Sn-40Pb (0 and 0.5wt.% Cu) solders, with emphasis on the roles of the Cu-Sn intermetallic layer thickness and the roughness of the interface between the intermetalic layer and solder. The shear strength test was performed for as-soldered solder joints with various soldering reaction times up to 4 min. The addition of Cu to the pure Sn solder results in an enhanced growth of the intermetallic layer whereas the effect of Cu addition to the Sn-40Pb solder is primarily on the reduction of the roughness of the intermetallic/solder interface. The critical thickness of the intermetallic layer for a maximum shear strength depends on the solder materials, which was measured to be ~ 2.3 $mu extrm{m}$ for Sn-Cu solders and ~ 1.2 $mu extrm{m}$ for Sn-Pb-Cu solders. The shear strength at the critical intermetallic layer thickness seems to increase as the intermetallic/solder interface becomes rougher. This is in accordance with the observation that the sheared fracture occurred initially within the solder tends to shift towards the intermetallic/solder interface as the intermetallic layer grows above the critical thickness.