In the present work, an attempt is made to predict the minimum blank holding pressure required to avoid wrinkling in the flange region during axisymmetric deep drawing process. Thickness variation during the drawing is estimated using an upper bound analysis presented in this paper. The minimum blank holding pressure required to avoid wrinkling at each punch increment is obtained by equating the energy responsible for wrinkling to that which suppresses the wrinkles. The predictions of the developed model are validated with the published numerical and experimental results and are found to be in good agreement. Parametric study is then carried out to study the influence of some process variables on the blank holding pressure to avoid wrinkling. © 2007 Elsevier B.V. All rights reserved.