The effective algorithm for automatic marking has been studied based on the mathematical and computational principles. The geometric and alphanumeric data are defined from the pattern information inputted through the digitizer and organized into the pattern database. The geometric pattern data of irregular polygons are converted to grid data structure. The grid allocation algorithm makes it possible to avoid any overlapping between the patterns without time taking complex calculations. For the automatic allocation we define an objective function, which is composed of four factors obtained from the area data including enclosure area, rectangular area, X-enclosure area, Y-enclosure area, and shape match area. The optimum position of the pattern was determined from the minimum vague of the objective function.