Part II of the present study focuses on the yield point phenomenon, a discontinuous transition from the apparently elastic to the elastic-plastic regime for basal [C, (0001)], rhombohedral [R, (1 012)] and prism [A, (12 10) and M, (101 0)] planes of sapphire (Al2O3) under spherical contacts. The yield point mechanisms are predicted by supplementing the analysis presented in Part I with a criterion for the yield point transition. The proposed criterion accounts for the low-symmetry structure of sapphire. The resulting theoretical predictions are compared with experimental results. This comparison focuses on the effects of surface orientation and loading rates on the yield point load and on the peculiarities of yield point mechanisms, as reflected in the acoustic emission (AE) signals associated with the yield point. For the C plane, the availability of pyramidal and prism slip is expected to be a limiting factor for the yield point transition. Depending on the loading rate, either basal slip or basal twinning dominates the yield point mechanism for the M plane. For the A plane, the yield point is determined by basal slip. For the R plane, a yield point mechanism involving rhombohedral twinning combined with basal or pyramidal slip is possible. Consistent with the experimental results, the highest and the lowest yield point loads are predicted for C and R planes, respectively.