Digital photoelastic phase-shifting techniques have simplified photoelastic fringe analysis, yet the automated determination of the first principal stress orientation remains a critical challenge in data interpretation. In this study, an automated identification method for the first principal stress orientation in photoelasticity has been proposed by integrating mechanical principles with phase analysis. In planar polarized light fields, phase maps of principal stress orientation exhibit singularity-induced ambiguity, resulting in two possible solutions for the orientation of the first principal stress. To resolve this problem, the phase map is mathematically extended from [0, π/2] to (-π/2, π/2] for both ambiguity cases. By correlating the extended phase distributions of principal stress differences in the model with the fundamental mechanical characteristics, the correct orientation of the first principal stress is automatically identified by analyzing the average grayscale of the unwrapped isochromatic phase image. Experiments with multiple loading models have demonstrated the universality of the proposed method.