Expressions are derived for the phase and group velocities of plane rotational waves in elastic plates with displacement vector parallel to the surfaces of the plates and perpendicular to the direction of propagation. It is shown that in a double plate two types of transverse wave can travel along the plate, each type consisting of an infinite number of modes. The behaviour of the waves is illustrated by dispersion curves, computed for the lowest modes. The paper concludes with an investigation of the properties of Love waves in a surface layer, including a discussion of the behaviour of the minimum group velocity, discovered by Jeifreys (1), for which a lower bound is found.