It has been shown recently that an acoustic wave which is nearly polarized in the shear horizontal direction can exist in thin plates of arbitrary elastic materials if the ratio h/λ (h is the plate thickness, λ the acoustic wavelength) is less than unity. We refer to this as a QSH (quasi-shear-horizontal) acoustic wave. Preliminary results showing attractive properties of this wave have been published. This paper presents detailed theoretical and experimental investigation of QSH waves in thin plates of lithium niobate. Results confirm that the QSH wave provides a number of attractive properties for use in sensing and signal processing applications. These include the following: (i) a phase velocity nearly constant for all values of h/λ; (ii) the ability to propagate in contact with a liquid medium and (iii) a very high value of electromechanical coupling coefficient. Experimental measurements of phase velocity and coupling coefficient are found to be in good agreement with theoretical calculations. The influence of a biasing electric field on the propagation of QSH waves has been calculated. It is shown that biasing voltages of less than 200 V can produce fractional time delay changes greater than 0.15% in QSH wave delay lines fabricated on 10 µm thick lithium niobate plates.