Almost all empirical formulae for estimation of blank-holding force (or pressure) proposed thus far are examined with respect to circular cup drawing from circular blanks. A theoretical formula proposed by Kawai is checked to find that it gives a too low value in a practical Sense. There exists no formula for estimation of blank-holding force to prevent flange wrinkling in the case where the circular cup is partially drawn from irregularly shaped blanks, and especially where the square cup is drawn from square or circular blanks. A new empirical formula for such cases including, of course, circular cupping from circular blanks, is proposed. By many experiments, formula is verified to be quite useful from the viewpoint that the blank-holding force should be the minimum necessary so as to prevent wrinkling. The effective area of the irregularly shaped blanks for estimation of blank-holding force is also discussed.