ASTRO-E Hard X-ray Detector (HXD) is characterized by well-type phoswich counters in a compound-eye configuration which reduce the X-ray and non X-ray background to lower level than any other past hard X-ray missions. When operating in Low Earth Orbit, the expected background of the HXD is an order of 10-5[counts/s/keV/cm2], mainly caused from the radioactivity induced within the detector materials by nuclear interactions with geomagnetically trapped protons. Results are presented from measurements of induced radioactivity in two phoswich scintillators, GSO and BGO, irradiated by mono-energetic protons at an accelerator facility. Radiation transport computer codes are used to build the detector response functions against emissions from decays of spallation products. Based on the comparison of experimental and simulation results, the activation background level of HXD in the orbit is estimated.