A machine for processing lateral edges of glass plates, plates of stone material or plates of synthetic material, the machine comprising: - a stationary support structure, - a group of plate gripping members, configured to hold a plate in a horizontal position during the plate processing, - wherein the group of plate gripping members is carried by a carriage movable at least in a plate conveying longitudinal direction, - a stationary machining unit for machining a lateral edge of the plate, the unit being carried by said stationary supporting structure and including a series of grinding tools aligned along the conveying longitudinal direction, in such a way as to engage in succession a lateral edge of a plate that advances along said conveying longitudinal direction, - wherein with said carriage carrying the group of plate gripping members, an electronically-controlled actuator device is associated, configured to move the carriage along said conveying longitudinal direction, said machine being characterized in that the plate gripping members are adjustable in position with respect to the carriage, and relative to each other by means of electronically-controlled actuator devices, and in that the machine comprises an electronic controller configured to adjust the position of the gripping members before processing the plate, as a function of the size and/or shape of the plate, so as to arrange the gripping members so as to ensure that the plate is firmly locked in a horizontal position on the carriage during processing of the plate, and in that the group of plate gripping members is rotatably supported by the carriage around a vertical axis, and is configured to be oriented around this vertical axis by means of an electronically-controlled actuator device, in such a way that after processing of a lateral edge of a plate, the plate can be brought to a position out of interference with the grinding tools of the stationary machining unit, and can then be rotated around said vertical axis and returned to a starting position with respect to the stationary machining unit, for subsequent processing of another lateral edge of the plate by means of said grinding tools of the stationary machining unit. - a stationary support structure, - a group of plate gripping members, configured to hold a plate in a horizontal position during the plate processing, - wherein the group of plate gripping members is carried by a carriage movable at least in a plate conveying longitudinal direction, - a stationary machining unit for machining a lateral edge of the plate, the unit being carried by said stationary supporting structure and including a series of grinding tools aligned along the conveying longitudinal direction, in such a way as to engage in succession a lateral edge of a plate that advances along said conveying longitudinal direction, - wherein with said carriage carrying the group of plate gripping members, an electronically-controlled actuator device is associated, configured to move the carriage along said conveying longitudinal direction, said machine being characterized in that the plate gripping members are adjustable in position with respect to the carriage, and relative to each other by means of electronically-controlled actuator devices, and in that the machine comprises an electronic controller configured to adjust the position of the gripping members before processing the plate, as a function of the size and/or shape of the plate, so as to arrange the gripping members so as to ensure that the plate is firmly locked in a horizontal position on the carriage during processing of the plate, and in that the group of plate gripping members is rotatably supported by the carriage around a vertical axis, and is configured to be oriented around this vertical axis by means of an electronically-controlled actuator device, in such a way that after processing of a lateral edge of a plate, the plate can be brought to a position out of interference with the grinding tools of the stationary machining unit, and can then be rotated around said vertical axis and returned to a starting position with respect to the stationary machining unit, for subsequent processing of another lateral edge of the plate by means of said grinding tools of the stationary machining unit.