A simple three-parameter transversely isotropic (TI) model is presented as a reasonable first approximation for the elastic behavior of a wide variety of shales. The model has the property that the zero-offset normal-moveout velocity is equal to the vertical velocity,a condition often approached by many shales. This constraint reduces the number of independent parameters to four. Under this assumption, a simple accurate approximation to the P-phase slowness surface may be found from which all oblique P-wave slownesses are predictable from just two speeds,the zero-offset normal-moveout velocity and the horizontal velocity. When seismic exploration data is confined to compressional waves recorded in a rather narrow aperture, such a TI medium will ‘appear isotropic’. A further constraint on the model parameters,reducing the number of independent parameters to three, connects the behavior in the horizontal plane to the behavior in the vertical plane. It allows for a generalization of the Lame parameters to the case where the TI anisotropy is due solely to the existence of two shear moduli, one vertical, the other horizontal. These simple models for shales behave as a TI medium equivalent to an isotropic medium stiffened by the inclusion of horizontally bedded thin rigid plates.