Based on equivalent transformation by means of mathematically rigorous analytics, the stress analysis of heavy cross-sectional, non-homogeneous Functionally Graded Composites (FGCs) has been performed by the layering calculation model in axis-symmetrical mechanics problems. The partially calculated results of the non-homogeneous layered thick-walled metal tube are similar to the design and practice of machine forging moulds manufactured with special welding electrodes developed by the German Capilla Company. The analysis is used complementary to the investigation of the quantitative analysis of thermo-mechanical properties, or the so-called anti-design and the optimization of the graded structure for FGCs.