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We realise a circular gray-field polariscope to image stress-inducedbirefringence in thin (submicron thick) silicon nitride (SiN) membranes andstrings. This enables quantitative mapping of the orientation of principalstresses and stress anisotropy, complementary to, and in agreement with, finiteelement modeling (FEM). Furthermore, using a sample with a well known stressanisotropy, we extract a new value for the photoelastic (Brewster) coefficientof silicon nitride, $C \approx (3.4~\pm~0.1)\times~10^{-6}~\mathrm{MPa}^{-1}$.We explore possible applications of the method to analyse and quality-controlstressed membranes with phononic crystal patterns

Polarimetric analysis of stress anisotropy in nanomechanical silicon nitride resonators