In this paper, the authors have proposed the stress function which can be applied to explain the crack mechanism for concrete structures by expanding materials or swelling of reinforcing bars due to corrosion. The analytical model is an infinite elastic plate under uniform compressive stresses with a circular hole which has radial cracks at the edge. Applied loads are uniform loads in the direction of cnlarging the diameter at the boundary of the hole. The function can express a process zone with smooth finite stress concentration at tips of the cracks.