We carried out in situ REM-RHEED (reflection electron microscopy-reflection high-energy electron diffraction) observations of the inner cylindrical Si surfaces to study surface structural phase transitions on various high index surfaces in the UHV condition. We observed reversible structural phase transitions that were suggested to be the roughening transitions on the high index surfaces. The transition temperatures are about 1000 degrees C, 880 degrees C, 780 degrees C, 805 degrees C, 820 degrees C and 770 degrees C for the (119), the (117), the (114), the (331), the (551) and the (320) surfaces, respectively. The results on the (119), the (117) and the (114) surfaces indicated that the roughening transition temper-ature decreases monotonously with increasing off- angles from the (001) orientation.