As a first step to bend a glass along a line traversing the plate, external heat is applied to the glass plate such that a narrow zone containing the entire length of the bending line is heated more intensely than the remaining area to reach a temperature at which the glass does not yet soften but exhibits an appreciable lowering of its electrical resistivity. Then an electric current is caused to flow through the glass in the intensely heated zone from one terminal of the bending line to the other terminal, until the glass is softened only in this zone, i.e. along the bending line by the Joule effect of the current. In this state, desired manner of bending is achieved by the use of a suitably shaped bending die.