Thermoelastic Stress Analysis (TSA) information is proportional to the change in the sum of the principal stresses. Since one often has to know the magnitude of individual stresses, additional experimental methods or data are frequently required to ‘separate the stresses’. This paper demonstrates the ability to evaluate individual stresses in a uniaxially-loaded finite plate with a central circular hole from TSA-recorded information without supplementary experimental data. Measured temperatures are combined with an Airy stress function and some limited traction-free conditions. The present technique does not presuppose knowing the external geometry or boundary conditions, overcomes traditional difficulties of unreliable edge data, and reduces the number of coefficients needed by satisfying the traction-free conditions analytically on the edge of the hole. Attention is paid to determining an appropriate number of the real (not complex) Airy coefficients.