This paper describes an apparatus for forming an angled convex surface at the ferrule endface by polishing the ferrule endface utilizing an elastic polishing plate performing orbital and rotational motion. When the diameter of the ferrule tip was greater than approximately 0.4 mm and when the Shore hardness of the elastic plate was approximately softer than 95, the formed convex radius on the ferrule endface was found to be an unique function of both the deformed depth of the elastic polishing plate and the diameter of the ferrule tip. The backreflection of the light beam from the polished optical fiber endface was as low as less than 064 dB for all tested samples when singlemode optical fibers were polished at a slanted angle of 8 degrees.