The frame of this work is the variability and sensitivity analysis of after-springback shape of deep drawn metal sheet using numerical models.We focus our interest on the propagation of the randomness in input (process or physical parameters) to the after-springback shape variability and sensitivity. As potentially numerous samples on a small variation range on the input process and physical variables may be involved, the underlying model has to reach simultaneously high performances in terms of computational costs, and accurate prediction of after-springback shape for small variations of the inputs. We show that the use of a full Finite Element Model is inappropriate, and propose an alternative two-pronged methodology to address these challenges. The deep drawing simulation process is performed using an original low cost semi-analytical approach based on a Bending-Under-Tension model exhibiting a high accuracy for small random perturbations on the input parameters and low computational cost. The springback variability and sensitivity analysis of the process is based on an advanced use of the Polynomial Chaos Expansion from which the approximated probability density function and Sobol’ indices of the springback shape parameters are computed at low costs.