This research paper has used a three-dimensional approach that combines Finite Element Analysis, the famous three-factor Design of Experiments by Taguchi, with the third dimension. An idea to optimize a Lithium (Li) and Lead (Pb) based Toroid is presented as they are known hazardous materials. The approach emphasized generating different run orders by a parametric variation of outer diameter, thickness, and base metal on the minimum and maximum specifications. Based on the Design of Experiments, the calculated run orders were modelled and simulated under the specified loading conditions to select the best combination of parameters. The analytical stresses generated in the combinations were compared with the numerical counterparts for model validation. On-Mises stress and deformation results from the simulation were analyzed to select the optimized design of Toroid structure and the final shape was modelled accordingly. The analytical and numerical stresses also showed good agreement with each other, supporting the validity of the presented approach. The method effectively models such specimens before fabrication, so that all material and geometric aspects can be finalized before risking physical contact with the actual worker.