We analyze the force on a point charge moving at relativistic speeds parallel to the surface of a uniaxial dielectric. Two cases are examined: a lossless dielectric with no dispersion and a dielectric with a plasma-type response. The treatment focuses on the peculiarities of the strength and direction of the interaction force as compared to the isotropic case. We show that a plasma-type dielectric can, under specific conditions, repel the point charge. editor's choice Copyright (C) EPLA, 2013