Abstarct: Investigation of the stress distribution in plates with discontinuous for prevention of failure structures is one of the most important issues in design of engineering. Hence, in this thesis, stress analysis of isotropic plates with two regular holes is studied. The analytical method wich is employed is baxsed on complex variable method, Schuartz’s method and a conformal mapping function. The Cauchy integral techniques are used to compute the integrals obtained in solving. The usability of this method is determined by mapping the out of region of two holes to out of a unit circle. According to alternating method, a convergent criterion is presented to determining the number of iterations. The ultimate stress functions for computing the stress distribution around two cut outs are obtained by using superposition principle and adopting summation of stress functions in all of iterations. The problem solving is done by supposing the plane stress conditions. The dimension of two holes in comparison to the dimension of plate considered small enough so that the plate can be assumed as infinite. Loading on the edge of the plate is assumed uniaxial. For validating and illustration the accuracy of the presented analytical solution, the results obtained from this method are compared with those given in available literatures and those obtained from the finite element method that are carried out by using ABAQUS software. The effect of different parameters such as location of two holes and their distance, bluntness of holes, aspect ratio and orientation of holes, on the stress distribution are investigatedand and the appropriate range of these parameters and suitable sort for location of two holes in plate which leads to reducing the stress values are determined by using obtained result.