This study aims to clarify the process conditions of the UO-tube of a sheet metal of steel. It provides a model that predicts not only the correct punch load for drawing, but also the precise final shape of products after unloading, based on the tensile properties of the material and the geometry of the tools used. An elasto-plastic incremental finite-element computer code, based on an updated Lagrangian formulation, was developed to simulate the UO-tube process of sheet metal; the results are compared with corresponding experimental results. Special care was taken to formulate accurate boundary conditions of penetration, separation and alternation of the sliding-sticking state of friction, as the contact conditions between the tools and the sheet varied throughout the entire processes of U-bending and successive O-bending. Calculated sheet geometries and forming force agree well with experimental data. In particular, selective reduced integration was adopted to formulate the stiffness matrix. The extended r-minimum technique was used to deal with the elasto-plastic state and contact problems at the tool-metal interface. A series of simulations were performed to validate the formulation in the theory, leading to the development of the computer codes. The whole deformation history, the distribution of stress and the distribution of strain during the forming process were obtained by carefully considering the moving boundary condition in the finite-element method. The simulation demonstrates clearly the efficiency of the code to simulate various bending processes that proceed under complicated deformation- and contact-history.