Abstract: When two or more surface cracks are present on an agingstructure the structure damage is accelerated. A finite thickness plateunder remote tensile surface traction with two semi-elliptical surfacecracks of different geometric dimensions and configurations in closevicinity is used as a model. To calculate the effect of vicinity crack onthe reference crack, the three-dimensional finite element method is used.Firstly the relation between stress intensity factor, at reference point(\theta = 0, \pi/2, \pi ) on reference crack front, with the cracksize is obtained through parametric analysis. After getting the stressintensity factor K and K' (where K and K' are the stress intensity factor with and without interaction of the crack inthe vicinity respectively) the effect factor \betaof vicinity crack to reference crack is calculated where \beta =K'/K.Finally the nonlinear relation is set up between crack dimensions andlocation with effect factor \betaby Neural Network. The result provides theoretical reference in practice toanalyze the aging structure with multiple surface cracks.