In this paper the variation of interface stress intensity factors is considered under arbitrary material combinations for several problems such as central internal interface cracks, periodic interface cracks, and edge interface cracks. The stress intensity factors for all these problems have been determined in terms of Dundurs’ parameters α, β by the application of FEM in the authors’ previous papers. In this paper, the variations of the stress intensity factors for all these problems are discussed under arbitrary α, β, then the maximum and minimum values of dimensionless stress intensity factors FI,max, FII,max, FI,min, FII,max are indicated on the map of α, β. As an example, it is found that FI,max always appears when (α, β)= (0.2,0.3), and FI,min always appears when (α, β)= (1,0), for the central internal interface cracks independent of crack length.