In continuum mechanics, a yield surface defines the boundary in stress space between elastic response and the onset of plastic flow. In two-dimensional Lennard–Jones model glasses, we construct local analogues of this surface and show that their angular dependence is dominated by regions with a positive second derivative of the yield stress with respect to the loading angle. Most of these regions are associated with characteristic non-affine rearrangements and are well described by a combined Schmid–Mohr–Coulomb criterion parameterized by a weak-plane orientation, an intrinsic critical stress, and a pressure sensitivity. The resulting parameter statistics characterize how the population of discrete yielding features encoded in the amorphous structure varies with the preparation protocol.