Multiple site damage (MSD) is the occurrence of small fatigue cracks at several sites within aging aircraft structures. Focusing on this typical structure, an analytical method for calculating the stress intensity factor (SIF) of an infinite plate containing multiple holes was introduced in this paper. The properties of complex variable functions are used to evaluate the stress function. The approximate superposition method is applied to solve SIF problems on multiple holes. Some numerical examples of radial cracks appearing at the boundary of two circular holes are examined by this method. By comparing the analytical and finite analysis results it was realized that the analytical results are accurate and reliable. This modified analytical method is easier to apply than traditional analytical method and can provide SIF solutions for an infinite plate containing multiple holes.