Display omitted •Unstable mode for crack in hcp-Mg is studied with the atomic elastic stiffness.•The mode is specified with the principal strain axis for negative eigenvalue atoms.•Basal plane crack has symmetric mode and actually shows unstable propagation.•Unstable mode for dislocation emission is also captured in the prismatic crack.•Crack tip singularity deviates from the linear facture mechanics by unstable atoms. As a series study discussing local deformation by the atomic elastic stiffness, Bijα=Δσiα/Δεj, various molecular dynamics simulations are performed on the basal, prismatic and pyramidal cracks in hcp Mg; and their different deformation behaviors are discussed by the 1st eigenvalue of BijαΔεj=ηαΔεi and their principal axis of the eigenvector {Δεi} at each atom point. The basal and pyramidal cracks show brittle cracking and the crack tip stress coincides with the magnitude of the σyy=KIC/2πr in the linear fracture mechanics, despite of the different conditions of single crack vs. periodic crack array. In the basal crack, the principal axes of ηα(1)<0 atoms clearly show symmetrical deformation mode against crack plane. The pyramidal crack propagates in the 30° tilted adjacent pyramidal plane, and ηα(1)<0 atoms emerge around the crack tip and the corresponding principal axes are often normal to the new crack surface. On the other hand, the prismatic crack shows dislocation emission and tip blunting. ηα(1)<0 atoms widely emerge in butterfly shape around crack tip before the stress–strain peak or the onset of dislocation emission. There is no remarkable structural change in these ηα(1)<0 region; however, the material property or local stiffness is clearly different from the surrounding media so that the stress distribution on the crack plane remarkably deviates from the continuum theory. The principal axes of these atoms are not in the crystal orientation but in 45° against loading axis; this difference possibly prevents the structural change. The trigger of dislocation emission is captured by the principal axis of ηα(1)<0 atoms, which is located on the tip surface and oriented in the slip direction.