A glass plate cutting machine 1 includes a cutter wheel 4 for forming a cut line 3 on a glass plate 2; a moving means 5 for moving the cutter wheel 4 along a cut line 3a which has been preset and is to be formed on the glass plate 2; a resiliently pressing device 6 for resiliently pressing the cutter wheel 4 against the glass plate 2; and a control unit 7 for controlling the resiliently pressing device 6 so as to alternately change over the intensity of a resiliently pressing force of that cutter wheel 4 with respect to the glass plate 2 in the movement of the cutter wheel 4 by the moving means 5.