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In this paper, the problem of linear elastic buckling of a simply supported rectangular plate, with a single circular cutout, subjected to uniform uniaxial edge compression is considered. The design objective is the maximization of the buckling load by determining the optimal location of the cutout. To accomplish that, a MATLAB routine coupled with finite element computation in ANSYS is employed. The study shows that the position of the center of the circular hole for the maximum buckling load remains always on the longitudinal centerline of the plate. However, the optimal center positions along this longitudinal axis for a given cutout size have great dependence on the aspect ratio of the plates. These optimal positions are reported for various values of plate aspect ratios and cutout sizes. These results are important from a design perspective and will be useful for design purposes in the future.