The transverse component of the seismic phase Sn is considered in terms of normal mode propagation of Love waves. Calculations of dispersion, attenuation and particle amplitude versus depth are presented for a realistic model of oceanic structure which includes the effects of sphericity and the upper mantle zone of low velocity and high attenuation. We find modes with group velocity maxima near the Sn velocity of about 4.7 km/sec, and with attenuation sufficiently low to explain the predominance of short-period (about 1 sec) motions of Sn at epicentral distances up to 35° to 40°. For these modes, the particle displacements are largely restricted to depths above the low-velocity zone of the upper mantle. These modes are found for a structure in which velocities in the uppermost mantle lid are constant as a function of depth; sphericity alone is sufficient to provide a “wave guide” for Sn. The most interesting result of the calculations is that at periods longer than about sec, modes with group-velocity maxima near 4.7 km/sec have substantial particle displacements in the low-velocity, low-Q zone in the upper mantle and are thus subject to severe attenuation. The results therefore indicate a filtering effect, which could explain the well-observed predominance of short-period motions of Sn. The particle displacement profiles calculated for the oceanic case also help to explain the efficiency with which Sn is excited by intermediate-depth sources, and provide a basis for accounting for the conversion of Sn into Lg across a continental margin.