Dispersion curves, surface displacements, and displacement profiles over the plate thickness are numerically calculated for acoustic plate modes, propagating in fused and Y-rotated, X-cut quartz samples with thickness h= in the range 0-4.5 (h, thickness; , wavelength). The Anisimkin Jr.' modes with velocity vn close to that of longitudinal bulk wave v L and the dominant longitudinal displacement u1 distributed uniformly through the plate thickness are found in quartz crystals with cut angles = 120 -140 and plate thickness h= = 0-0.36, 0.94-1.78, 2.32-3.08, and 3.64-4.44. The same modes in fused quartz are not found, except in a narrow region near zero thickness.