The anisotropy of heat conductivity that develops on uniaxial stretching of amorphous high polymers has been examined theoretically and experimentally. Experimental measurements on oriented polystyrenes and polymethylmethacrylates show a linear increase in conductivity (parallel to stretching) with increasing elongation. The slope of the relationship is sensitive to the molecular weight distribution of the polymer and the stretching conditions (temperature). The observations are discussed in relation to current theories of heat conduction in polymers.