Abstract Simulation of complex ring profiles using an improved Upper Bound Elemental Technique (UBET) is presented in this paper. The profile of the ring is approximated with a collection of triangular-prismatic and rectangular-brick elements. A generalized solution procedure is proposed to find the optimized kinematically admissible velocity field for the unique three-dimensional material flow experienced in shape rolling. Close agreement between numerical results obtained from simulations and available data for profile ring rolling has been observed for high-temperature aerospace materials. It has been demonstrated that the complex ring profiles used in aerospace industry can effectively be simulated using the current software tool.