The low density of the magnesium alloy AZ31 makes it valuable for low weight components. The main limitation for industrial applications is the poor formability of sheets during deep drawing type processing. This is linked to the fibre crystallographic texture resulting from rolling. The objective of the present work is to modify the sheet texture through asymmetrical rolling. It has appeared that the asymmetry promoted by monitoring the roll speeds separately induces plastic instabilities through shear banding. The physical mechanisms involved in the instability were analysed with the help of orientation imaging techniques on transmission electron (ACOM/TEM) and scanning electron (EBSD/SEM) microscopes as well as with X-ray measurements. It is concluded that the shear resulting from the asymmetry in roll speeds promotes a dramatic increase of basal slip that neither twinning nor the activities of other slip systems are able to compensate. Such activity induces strain localisation and premature failure of the material.