Recent experiments have shown failure in flip chip micro solder joints induced by electromigration. This paper proposes a computational model to simulate the evolution of micro and sub-micro scale solder joints due to electromigration induced diffusion. Complicated morphological changes of the solder bump and multiple mechanisms cause a computational challenge. This is addressed by employing a diffuse interface model with multiple concentrations. To efficiently resolve complications, a semi-implicit Fourier spectral scheme and a biconjugate-gradient method are adopted. Results have demonstrated rich dynamics and solder breakage at the interface on the cathode side.