Display omitted •Twinning in Fe is discussed with the positiveness of atomic elastic stiffness (AES)•Negative AES layers or unstable bands appear just before the stress drop•The first twin initiates at the point where the negative AES appears first•Multiple twins are formed at the unstable bands after the stress drop As a series study that discusses local instability by atomic elastic stiffness, Bija=Δσia/Δεj, molecular dynamics simulations of simple shear on Fe perfect lattice are performed to discuss twin deformation. In the simulation of extremely low temperature of 0.1K, many twin boundaries are nucleated in a periodic slab cell of stacked (1¯1¯2) planes just after the stress drop or elastic limit under shear. The 1st eigenvalue ηa(1) of the 6×6 matrix Bija shows fluctuation in each (1¯1¯2) planes just before the elastic limit. At the stress-strain peak, ηa(1)<0 or unstable layers emerge and twin deformation occurs at these unstable “band” in the simulation cell. The period of the ηa(1) fluctuation is almost constant even if the cell size is expanded in the 1¯1¯2 and 11¯0 direction, while the unstable band arrays tilt normal to the diagonal line of the simulation cell, under the cell expansion in the 111 direction. At the elevated temperature of 300K, the simultaneous periodic band never appears but a few unstable bands appear locally in time sequence and bring twinning there.