Springback assessment for sheet metal forming processes is a challenging issue which requires to take into account complex phenomena (physical non linearities and uncertainties). We highlight that the stochastic analysis of metal forming process requires both a high precision and low cost numerical models and propose a 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 with a good accuracy for small random perturbations of the physical and process parameters. The springback variability analysis is performed using an efficient stochastic metamodel, namely a sparse version of the polynomial chaos expansion.