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A stress integration algorithm is provided for a novel homogeneous-yield-function-based anisotropic hardening (HAH) model. The new model is an extension of the original HAH model that describes cross-hardening or softening of a sheet metal under an orthogonal strain path change. A semi-explicit integration scheme for the stress update is utilized to efficiently handle the gradient of the distorted yield surface during complex strain path changes, as originally proposed by Lee et al.(2012). Validations of the algorithm developed were conducted by comparing the predicted stress–strain curves of dual-phase (DP) 780 and extra-deep-drawing-quality (EDDQ) steels with experimental stress–strain responses observed under cross-loading conditions. Finally, the accuracy of the proposed finite element (FE) formulations was assessed by r-value prediction and preparation of iso-error maps.