Abstract: In a machine and in a method for processing lateral edges of glass plates, plates of stone material, and plates of synthetic material, there is a group of gripping members of the plate configured to hold a plate in a horizontal position. The plate is caused to advance in a conveying longitudinal direction, in such a way as to bring a lateral edge of the plate to engage in succession an aligned series of grinding tools forming part of a stationary machining unit. In one example, the group of gripping members of the plate is rotatably carried around a vertical axis by a carriage, which is movable in the conveying longitudinal direction and in a transverse direction orthogonal to the longitudinal direction. The gripping members are carried by the carriage in such a way as to be adjustable in position, by means of electronically-controlled actuator devices, with respect to the carriage and relative to each other.