Piezoelectric acoustic boundary waves in the structure of multilayer thin films/electrode/piezoelectric substrates Waves propagating along a perfectly conducting plane embedded in a piezoelectric medium are investigated. The theory of such waves is given, and numerical calculations are described. The conditions of existence and the properties of the waves are presented for trigonal lithium niobate, langasite, and cubic dilithium tetraborate. The numerical analysis shows that the waves exist for many orientations of the conducting plane with respect to the crystallographic axes, and for many directions of propagation. The wave velocity is close to that of the slowest bulk wave for the same direction, and the piezoelectric coupling coefficient can be as high as 3.60% for lithium niobate, 0.25% for langasite, and 1.60% for dilithium tetraborate.