This paper provides a detailed study on surface acoustic wave (SAW) induced acoustic streaming and pumping, focusing on the effects of the wave mode and surface modification. SAW devices with wavelengths of 32 and 64 µm were fabricated on 128° Y-cut lithium niobate substrates with aluminium interdigitated transducers. A higher order harmonic mode wave appears in addition to the fundamental Rayleigh wave for samples with metallization ratios less than 0.6. Both waves have demonstrated the ability to induce acoustic streaming and to pump liquid. A high streaming velocity, and hence a high mixing efficiency and a higher acoustic force, can be obtained using the fundamental Rayleigh wave as the high harmonic waves have large propagation losses. A linear relationship between the streaming velocity and RF signal voltage has been obtained, and effective mixing can be achieved. An acoustic wave has also been utilized to manipulate and pump droplets with sizes up to 5 µl, and a moving speed of ~1.4 cm s−1 has been obtained on an octadecyltrichlorosilane-treated SAW device using a signal voltage of 40 V.