The purpose of this paper is to research problems of cracks at a circular hole, which is a common crack configuration in aircraft structures. The Muskhelishvili complex function method and the Cauchy integral method are combined to develop crack surface displacement equation for two cracks with arbitrary length emanating from a circular hole in an infinite plate under pressure on part of crack surface, and calculate the crack-surface opening displacements for two cracks with arbitrary length emanating from a circular hole. When two cracks are symmetric, the calculated results were compared with the weight function method, the maximal relative error is 16.21%. The results show that the complex variable function method and the Cauchy integral method used to calculate crack surface opening displacements can be applied for two-symmetric（or asymmetric） cracks emanating from a circular hole in an infinite plate. The present study provides a research foundation for fatigue crack closure and crack opening stress analysis for double cracks with arbitrary length emanating from a circular hole.