Abstarct: In this thesis, investigates the optimum design of isotropic finite plates with different non-circular cut-outs subjected to in-plane loading (uniaxial tensile, biaxial, and pure shear load). This objective is pursued by a gray wolf optimization algorithm. The important features of this algorithm include flexibility, simplicity, short solution time, and the ability to avoid local optimums. The objective function used for in this algorithm seeks to minimize the value of stress concentration factor around different cut-outs. The method used for the calculation of stress concentration is baxsed on analytical solution of Muskhelishvili complex variable and conformal mapping with plane stress assumption. The plate is assumed to be isotropic, linear elastic, and finite. To calculate the stress function of a finite plate with a square cutout, the stress functions in finite plate are determined by superposition of the stress function in infinite plate containing a square cutout with stress function in finite plate without any cutout. Using least square boundary collocation method and applying appropriate boundary conditions, unknown coefficients of stress function are obtained. Moreover, finite element numerical solution is employed to examine the results of present analytical solution. Numerical results are in good agreement with the results of the present analytical solution. Results show that by selecting the aforementioned parameters properly, less amounts of stress could be achieved around the non-circular hole leading to an increase in load-bearing capacity of the structure.