Propagation of shear horizontal waves in class C6v piezoelectric plates with polar (or sixfold) axis in the transverse horizontal direction is analyzed for various boundary conditions: faces electrically free, shorted, or coupled to a thin homogeneous semiconductor plate. The case considered is that of identical physical conditions at the opposite faces, which permits the symmetric and antisymmetric waves to be treated independently. Of the above waves, the lowest modes behave as transverse surface waves at high frequencies, and the higher modes retain their oscillatory behavior in the thickness direction. Numerical solutions are obtained for amplification and phase velocity in PZT under different boundary conditions, and it is shown that the phase velocity can also be strongly dependent on the drift velocity of carriers in the semiconductor. The shapes of the dispersion and amplification‐frequency curves are also drift‐dependent, especially in the vicinity of cutoff.