A method for beveling a thin glass plate by simultaneously grinding an edge of the glass using multiple abrasive cup wheels, wherein the edge of the glass plate is extended from the fixturing device. The extension of the glass plate allows the glass plate to bend in response to forces applied by the abrasive cup wheels, thereby reducing the sensitivity of the grinding process to variations in position of the abrasive wheels. The axes of rotation of the abrasive wheels are separated by a distance selected to prevent deflection in the glass plate caused by a first abrasive wheel to influence the deflection in the glass plate caused by a second (adjacent) abrasive wheel.