A surface-plasmon sensor, in the attenuated-total-reflection configuration, is modeled by a glass-metal-dielectric-air structure, where a dielectric film with anisotropic permittivity models the material (or particulates) to be sensed. The laser beam, polarized in the plane of incidence, is obliquely incident on the glass-metal interface from the glass side. At a particular angle of incidence θr, the laser beam excites a surface plasma wave at the metal-dielectric interface, and the reflectivity is at a minimum. The minimum reflectivity angle θr increases linearly with the thickness of the dielectric film and is sensitive to the components of the permittivity tensor. The depth and half-width of the reflectivity minimum, however, remain practically unchanged.