We study the acoustoelectric effect in two-dimensional materials like transition metal dichalcogenide monolayers located on a nonpiezoelectric substrate and exposed to the Rayleigh surface acoustic waves. We investigate the behavior of the Hall component of the electric current density which appears due to the trigonal warping of the valleys in k space. We calculate the spectrum of the current density and study its dependence on the electron effective lifetime and density in the sample. We distinguish between the drift and diffusive components of the current and show which components turn out predominant. Furthermore, we compare the effect of the Rayleigh and Bluestein-Gulyaev acoustic waves, which appear if the sample is located on a piezoelectric substrate.