In a large bowl, cream the shortening with the sugar. Add the eggs and vanilla and mix well. Sift the flour and salt into the creamed mixture and stir in gradually. Chill dough for at least one hour.
Roll the chilled dough out to 1/8 inch thick and cut into desired shapes. Bake on an ungreased baking sheet for 6 to 8 minutes. Allow cookies to cool before decorating.