Based on the classical theory of surface diffusion induced by stress migration, a finite element program is developed for simulating the evolution of intergranular microcracks in copper interconnects. The numerical results show that there exists a critical value of the line width under the biaxial tensile stress state. When the line width is equal or less than the critical value, the intergranular microcrack will grow and split into three small microcracks along the grain boundary. When the line width is greater than the critical value, the microcrack will directly evolve into a cylinder. The splitting time of the intergranular microcrack reduces with the line width decreasing, which means that the decrease of the line width will accelerate the splitting process. Both the critical value of the stress and that of the aspect ratio decrease when the line width decreases, that is, the decrease of the line width is beneficial to the microcrack splitting. The critical values of the stress and the aspect ratio decrease when the ratio of the grain-boundary energy to the surface energy increases. And it is easier for the intergranular microcrack to split than the intragranular microcrack.