A finite element technique is used to study time-harmonic Love waves propagating in three-dimensional structures. As an illustration of the technique, the problem is solved for the restricted case of particle motion in one dimension. Two examples of Love waves in structures whose properties vary in the two dimensions perpendicular to the direction of propagation are presented for this restricted problem. It is shown that the velocities with which effects from a lateral boundary propagate appear to be of the magnitude of the P-wave velocity of the structures. It is also shown, for this restricted problem, that phase-velocity measurements made too close to a lateral boundary between two geologically distinct zones may produce values that are grossly incorrect.