Shear-induced instability of bilayer membrane systems has attracted much attention. One of the most interesting shear effects is a shear-induced structural transition from the lamellar to the multilamellar vesicle. In this review, we show two topics related to the non-equilibrium structural formation phenomena under shear; the influence of the triblock copolymer on the shear-induced multilamellar vesicle formation, and the shear quench-induced discontinuous size change of the multilamellar vesicle. In the first topic, we study the effect of the triblock copolymer on the shearinduced lamellar-to-multilamellar vesicle formation. Shear-induced multilamellar vesicle formation behavior is quite sensitive to the interaction between grafted polymer chains and surfactant bilayer membranes. Entropy based contribution to the modulus of bilayer controls the shear-induced multilamellar vesicle formation behavior. In the second topic, we study how the kinetic pathway on the size change process of the multilamellar vesicle is decided under shear. These studies will give us a hint how the soft matter systems change their structure under non-equilibrium states.