Abstract: A method for uniformly beveling an inside edge of a glass article having an opening at one end thereof includes the steps of: providing a plate having a peripheral shape generally corresponding to that defined by the edge of the glass article, the plate having a beveled edge containing an abrasive material; supporting the glass article so that its inside edge is in proximity to the beveled edge of the plate; and establishing contact between the glass article and the abrasive material. An orbital, undulatory motion is induced between the bevel plate and the glass article to abrade at least a portion of the inside edge of the glass article. An apparatus for practicing the method is also described and may be used for uniformly beveling the inside edge of CRT funnels and faceplate panels.