<p>A non-material shell finite element model is devised for the numerical simulation of industrial roll forming lines. The simulation model is designed to facilitate the time-efficient simulation of large forming lines and features: a mixed Eulerian–Lagrangian description of primary fields, shell finite elements based on the Kirchhoff–Love theory, a reduced stress-resultant plasticity model designed for bending-dominant forming operations of thin structures, a geometrically accurate penalty contact formulation to resolve the frictionless interaction in the forming gaps and a novel segmentation strategy. A Newton–Raphson scheme with operator split is employed to compute a sequence of quasi-static equilibria that gradually approach the steady-state solution; the Eulerian phase of the operator split accounts for the downstream transport of plastic variables through the non-material mesh. The novel segmentation approach features a cyclic marching strategy to perform sequential simulations of overlapping sub-models. It reduces the computational effort for large-scale models and facilitates parameter studies for designated parts of a forming line. Numerical results obtained for a benchmark problem with six forming stands demonstrate the excellent agreement of segmentwise simulations with the global simulation of the entire forming line. The scaling of the computation time with the length of a forming line is investigated to estimate the utility of the marching strategy for even larger configurations.</p>