The repression of wrinkling during sheet metal forming has been a significant issue in recent years. In order to provide a reliable and efficient tool to predict the critical blank holding force to prevent wrinkles, an axi-symmetric analytical model for flange wrinkling is introduced here. Using a conventional theory of the critical condition, the critical blank-holding force and wave numbers are numerically predicted. Comparison between the numerical and experimental results shows excellent agreement for various blank dimensions and materials.