We present a theoretical description and results of the first experimental observation of Bloch oscillations, Wannier-Stark ladders, and resonant Landau-Zener tunneling of surface acoustic waves in perturbed grating structures made of gold stripes on a LiNbO3 substrate. Our model provides a quantitative description of all the relevant features of the experimental observations, including multiple resonant Landau-Zener transitions between anticrossed surface acoustic Wannier-Stark states, which originate from neighboring acoustic minibands.