Two acoustic modes, which propagate in rotated YX-cuts of LiNbO3, were investigated as functions of rotation angle. The main characteristics of these modes, including polarization vectors, were determined first for free surface, and then analyzed as functions of Al thickness, in a substrate with uniform film or periodic grating. The behavior of typical Rayleigh-type and Love-type modes, which propagate in 128 degrees YX cut, is compared with acoustic modes propagating in 15 degrees YX cut. Velocity versus rotation angle dependences, calculated at different Al thickness, demonstrate gradual transformation of LSAW into the non-leaky SAW, with increasing Al thickness, and interaction between two SAW modes.