Teleseismic Pn waves are modeled as a sum of whispering gallery waves, which propagate in a waveguide composed of a simple high velocity mantle lid underlain by a low velocity zone. This model is able to account for those Pn wave propagation properties that are not dominated by scattering, i.e., their apparent velocity and lack of long period energy. Pn apparent velocity data constrain the P wave velocity gradient in the upper 100 km of mantle to be low; dvp/dz<0.001 s-1. The whispering gallery rays are shown to have significant amplitude (when compared to the direct P wave) and to have spectra that rapidly fall off at long periods. Yet this model cannot account for certain details of the observed Pn amplitude spectra. Most important among these is the spectral ratio of Pn to P, which the model underestimates by a factor of 10. Nevertheless, the model presents a useful framework for understanding some characteristics of Pn wave propagation and provides an estimate of the distribution of energy with depth in the Pn waves.