This study presents intensive numerical analyses of the ring elongation testing technique (RETT) used to characterize the 7175-T7351 aluminum alloy and St 37 carbon steel rings materials. Theoretical solutions were developed to predict the elastic properties of the materials of the ring using both curved and straight beam formulas. Besides, to predict the full deformation behaviors of the ring's materials, elastic, and elastic-plastic finite element analyses (FEA) were performed on the 2D and 3D ring models. Moreover, FEA were conducted to study the effects of ring dimensions, pin diameter, and ring shape on the RETT results. Modeling the ring specimens with plane stress elements and 3D-stress elements was done with the FEA commercial package (ABAQUS). Theoretical and the FEA results were then compared to the experimental results. The theoretically obtained elastic results accurately predicted the elastic properties of the ring materials. Furthermore, the FEA results successfully predicted the full deformation behaviors of the ring materials.