The author developed a mathematical model of thin sheet metal drawing processes in impulse and quasi-static forming conditions using the LS-DYNA finite-element complex. During the calculation, a gap magnitude between a holder and a die was varying and its influence on the forming process was studied. Forming limit diagrams of the considered processes allowed obtaining an overall view of wrinkling probability on the flange and center of blank. Moreover, the study showed a wrinkling probability dependence on strain rate and gap magnitude between the holder and the die. Thus, finite element calculation allowed making a comparison of the effective plastic strain magnitudes as well as considering the characteristics of the drawing processes, depending on the strain rate. As a result, favorable gap magnitudes between the holder and the die were determined for different strain rates.