A lithium tantalate single crystal substrate for a surface acoustic wave device that is a rotated Y-cut LiTaO3 substrate whose crystal orientation has a Y-cut angle of not smaller than 36° and not larger than 49° and which has such a Li concentration profile after diffusion of Li into the substrate from the surface thereof that the Li concentration at the surface of the substrate differs from that inside the substrate. A shear vertical type elastic wave whose main components are vibrations in the thickness direction and in the propagation direction and which is among those elastic waves which propagate in the X axis direction within the surface of this LiTaO3 substrate has an acoustic velocity of not lower than 3140 m/s and not higher than 3200 m/s.