Preheat oven to 425 degrees F (220 degrees C). Lightly grease cookie sheets.
In a large bowl, cream together the sugar and shortening until smooth. Stir in the molasses. Combine the baking soda, ginger,cinnamon and 3 3/4 cups of the flour; blend into the molasses mixture. Add more flour if necessary to make dough stiff enough to roll out. Use remaining flour to dust rolling surface. Roll dough out to 1/4 inch thickness and cut with cookie cutters.
Bake for 5 to 7 minutes in the preheated oven. remove from baking sheets to cool on wire racks.