An accurate description of the material yielding behavior is of great importance for a trustworthy prediction of complicated forming processes via numerical analysis. For metal sheets, the work hardening rate, in general, varies according to the loading directions and conditions due to the texture developed during cold rolling processes, and accordingly, the yield surface evolves with a variation of its shape and size during plastic deformation. The non-uniform evolution of the yield surface becomes a non-negligible issue especially for the materials showing the severe tension/compression asymmetry on the yielding behavior with respect to the loading direction. A primary concern here is that the advanced yield criteria previously developed normally feature an isotropic expansion of the yield surface which is determined at an initial yielding stage and thereby neglect the evident changes in the shape of the yield surface as implied by experimental tests. In this paper, a solution to the challenge of modeling a general criterion, which accurately describes the evolution of the anisotropy/asymmetry-induced distortional yielding behavior, is proposed using neither any interpolation nor optimization techniques for the calibration of the yield surface. The new criterion is proposed based on the Stoughton and Yoon (2009) criterion, which features non-associated flow rule, with the multiplication of two additional terms referred to as scaling and asymmetry functions. The proposed criterion was successfully applied to various types of metallic materials to validate its noticeable flexibility and general applicability in describing the anisotropic/asymmetric yielding behavior. An extensive comparison of the experimental results with the predictions from the proposed criterion reveals that the proposed criterion provides sufficient predictability on the subsequent evolution of the anisotropy/asymmetry-induced distorted yield surface for various metallic materials over a broad range of plastic strain level, strain rate, and temperature.