Abstract: A cracked metallic structure repaired with adhesive bonding composite patches is simplified using the superposition principle of the stress intensity factor (SIF), commonly used in linear elastic fracture mechanics. A Line-Spring model, based on a hypersingular integral equation, is developed according to the linear spring model for surface cracking. The hypersingular integral equation is then transformed to a system of linear equations by the second Chebyshev polynomial expansion method. Then, the SIF is expressed in terms of the displacement discontinuities of the crack surface. The numerical result of SIF for the crack tip correlates very well with the finite element computations based on virtual crack closure technique (VCCT). The two relevant key parameters for stress intensity factor (SIF), adhesive interface stiffness,, and the ratio of the patch stiffness to the plate stiffness,, are identified and discussed. The present mathematical techniques and analysis approaches are critical to the successful design, analysis, and implementation of bonded repairs.