The ability of pressurized circular membranes to approximate a paraboloid of revolution is investigated with the goal of designing a high-precision and lightweight solar dish concentrator. The optical performance of elastic and elasto-plastic deforming membrane materials is thoroughly analyzed by means of finite element structural modelling combined with Monte Carlo ray-tracing simulations using the yield strength, elastic modulus, and tangent modulus as parameters. The simulation results are verified experimentally by accurate scans of PET and aluminum membranes. They reveal that elasto-plastically deforming membranes can reach a peak concentration ratio of 3070 at a rim angle of 20 degrees -a 14-fold value vis-a-vis that of conventional elastic membranes while keeping strains at reasonable low level. Anisotropy detrimentally affects the aluminum membrane's performance, but optimal overstretching in the plastic regime can further boost its peak concentration ratio. (C) 2015 Elsevier Ltd. All rights reserved.