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Evaluating the coefficients of a relevant Airy stress function from measured temperatures (i.e., thermoelastic stress analysis, TSA) enables the determination of the individual stresses in an aluminum plate which contains a near-edge circular hole. The plate is supported along its edge from below and subjected to a concentrated top-edge load away from the hole. Imposing the traction-free conditions analytically, rather than discretely, on the edge of the hole significantly reduces the number of coefficients needed in the stress function, as well as the number of equations involved in the least squares process. The general technique, which is applicable to a wide range of engineering problems and materials (no model or coating is required, other than perhaps being painted flat black to enhance the uniformity and emissivity of the material), benefits from the availability of contemporary equipment capable of providing extensive amounts of data in a matter of minutes