<p>Two formulations of a fourth-order orthotropic yield function in plane stress have appeared in the literature, namely, Gotoh’s complete fourth-order homogeneous polynomial with nine coefficients and Yld2000-2d with eight material parameters and a stress exponent of four. Calibrated with the same three, five, seven, eight or nine independent experimental inputs, the similarities and differences between these two formulations of the fourth-order yield function in anisotropic plasticity modeling of four sheet metals are investigated in this study. It is shown that the fourth-order Yld2000-2d is not unique if the standard set of eight experimental inputs from three uniaxial and one equibiaxial tension tests are used for its parameter identification. Although Yld2000-2d formulation can be used for convexification of a calibrated but non-convex fourth-order polynomial function, the convexity-constrained least-square minimization is a better alternative to guarantee the convexity of a calibrated Gotoh’s yield function without reducing its total number of independent material parameters from nine to seven.</p>