The need for sheet metal forming using reconfigurable dies has increased due to rapid changes in part design to meet customer requirements, especially in the automotive industry. Reconfigurable dies have relatively low manufacturing cost compared with solid dies, and the same tool can be readily changed to produce different parts. Previous investigations have focused on avoiding defects without taking into account the effects of process on the quality characteristics of fabricated parts. This study investigated the influence of parameters, such as the elastic cushion thickness, coefficient of friction, pin size and radius of curvature, on the quality of parts formed in a flexible multi-point stamping die. The aim was to determine the optimum values of those parameters. Finite element modelling was employed to simulate the multi-point forming of hemispherical parts. Using the response surface method, the effects of process parameters on wrinkling, deviation from the target shape and thickness variation were investigated and the process parameters yielding the best product quality characteristics were obtained. The results show that pin size and radius of curvature have the greatest influence on wrinkling and deviation between formed and target shapes, while coefficient of friction, pin size and radius of curvature significantly affect thickness variation.