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With the aim of achieving stable operation of circular saws, this study finds the solution for the optimization problem that involves choosing a set of tensioning parameters in a rotating circular saw that is subjected to both a local temperature distribution and the in-plane plastic strain over a double annular domain. The solution for the in-plane forces is obtained on the basis of plate bending theory, and modal analysis for the out-of-plane behavior affected by the in-plane forces is performed. Numerical calculations are performed to investigate the effects of tensioning over the double annular domain on the natural frequencies. The optimization problem to maximize the natural frequency of the most critical mode with respect to the intensities, locations, and widths of tensioning is solved using a genetic algorithm, and the optimal tensioning parameters are determined at computational costs that are considerably lower than those required for 100% inspection.