This paper investigates the formation and the growth of the intermetallic compound (IMC) layer at the interface between the Sn3.0Ag0.5Cu Pb-free solder and the Cu substrate during isothermal aging at 150 °C. We measure the thickness of the IMC layer and the roughness of the solder/IMC interface, and these two factors are assumed to control the tensile behavior of the solder joints. First, it utilizes the tensile tests of the aged solder joints for analyzing the effect of the IMC growth on the tensile behavior of the solder joints. Then, the microcracking behavior of the IMC layer is investigated by finite element method (FEM). In addition, qualitative numerical simulations are applied to study the effect of the IMC layer thickness and the solder/IMC interfacial roughness on the overall response and the failure mode of solder joints. The experimental results indicate that when the aging time increases, both the thickness and the roughness of the IMC layer have a strong influence on the strength and the failure mode of solder joints. The numerical simulation results suggest that the overall strength of solder joints is reduced when the IMC layer is thick and the solder/IMC interface is rough, and the dominant failure mode migrates to the microcracks within the IMC layer when the IMC layer is thick and the solder/IMC interface is flat.