A theory on acoustic streaming generated by Lamb waves propagating in a thin composite membrane was developed. Using this theory, the mass-transport velocity in water, which is loaded on a 4-μm-thick membrane, due to Lamb waves at 4.7 MHz was calculated. The results are in good agreement with the experimental values measured by Moroney et al. [Appl. Phys. Lett. 59, 774 (1991)].