The method of construction and attestation of a numerical model of cold stamping of thin-walled products made of anisotropic metal sheet for the design of technological operations is proposed. The relations of the associated law of plastic flow with the Barlat flow function and isotropic strain hardening are used. The method of design and processing the experiment is proposed for their identification. The forming limit curve is approximated numerically by the Marciniak - Kuczynўski method, and for its identification it is proposed to use a failure test under uniaxial tension and press equipment as an experimental. To do this, a coordinate grid is applied to a flat blank by laser engraving, whose distortions near the zones of strain localization and failure of the vessel give additional points of the forming limit curve. The constants of the Peng - Landel potential are found to describe the elasticity of a polyurethane die under large deformations using tests for free and constrained compression. All tests according to the method were performed for low-carbon sheet steel DC04EK 0.7 mm and SKU-PFL polyurethane. A numerical model of the process in the LS-DYNA package is designed using material models from its library. The calculations according to the model were confirmed by experiment, for which the main deformations were determined by the distorted coordinate grid on the workpiece after each operation at the control points. The calculation of the sequence of stages of stamping, drawing and bulging of the workpiece in the production of the vessel with and without intermediate annealing is performed and the dangerous zones and mechanisms of their formation are determined.