To provide a method and an apparatus for engraving a scribe groove on the surface of a glass plate and to provide a technical means capable of splitting the glass plate only by a scribe step.

A roller blade 4 is pushed and rotated on the surface of the glass plate while the roller blade is vibrated in the direction generally orthogonal to the glass plate to engrave the scribe groove, so that the scribe groove has a perpendicular crack which is deep enough to eliminate a break step. For making the perpendicular crack deeper, it is effective to have a smaller diameter of the roller blade 4 and to slightly incline the direction of the vibration V in the traveling direction of the roller blade. The pushing pressure and the amplitude of the vibration of the roller is feedback-controlled to control the depth of the perpendicular crack. A vibrator to vibrate the roller blade is fixed only to a vibration-transmitting member for transmitting the vibration to the roller blade to be held. The vibration-transmitting member is held at one point, which is a node of the vibration of its intermediate part in the longitudinal direction.