Recent ductile damage models have in common that fracture strain is a function of stress triaxiality, η, defined as the ratio of mean to equivalent stress. Since the formulation for the equivalent stress depends on the chosen yield criterion, results for η are expected to differ, and deviations to increase with anisotropy. We therefore choose the highly anisotropic Zirlo for investigating this yield criterion-dependence and the evolution of η with strain. Analytical solutions for η are presented for 3 common yield criteria: Mises, Hill48 and Barlat89. Using digital image correlation (DIC) for local strain measurement in the fracture region, we extract Lankford coefficients for 0°, 45° and 90° and calculate η. Comparisons of results with analytical solutions for special cases (uniaxial tension, shear, plane strain) and with results for mildly anisotropic sheet metals shows the significance of the choice of the yield criterion for highly anisotropic sheets.