We performed measurements of the prompt radiation induced conductivity in thin samples of Alumina and Sapphire at the Little Mountain Medusa LINAC facility in Ogden, UT. Five mil thick samples were irradiated with pulses of 20 MeV electrons, yielding dose rates of 1E7 to 1E9 rad/s. We applied variable potentials up to 1 kV across the samples and measured the prompt conduction current. Analysis rendered prompt conductivity coefficients between 1E-10 and 1E-9 mho/m/(rad/s), depending on the dose rate and the pulse width for Alumina and 1E-7 to 6E-7 mho/m/(rad/s) for Sapphire.