Analytical determination of anisotropic parameters for Poly6 yield function

•The Poly6 yield criterion is analytically calibrated without any optimization method under associated flow rule.•Two types of calibrations are used: 1) the shear flow stress and the rb value; 2) the stresses under σxx = 2σyy and 2σxx =σyy.•The first calibration is very similar to the reported optimization-based calibration for Yoshida 2013 criterion and the second calibration method is close to Yld2000-2d prediction.•Both methods of calibrating the analytical Poly6 yield criterion are shown to describe the r-value and uniaxial yield stress directionalities accurately.•The proposed analytical method can be conveniently used for sheet metal forming simulation.