The tubes and pipes manufacturing industry characterizes the mechanical properties of their products with a wide selection of standards, but most of them are qualitative testing methodologies. To estimate the mechanical properties from a quantitative point of view there are limited options in standards. In that sense, the standard tensile test is the preferred alternative by the manufacturers, but this option limits the mechanical estimation for the longitudinal direction of the tube–pipe product. Particular efforts have been made to design an alternative mechanical testing procedure to characterize the mechanical properties in the hoop direction of pipes and tubes. The Ring Hoop Tension Test (RHTT) was designed to fill this gap, but it shows limitations related to the required tooling and the influence of the frictional contact between the tooling and the ring specimen. In the nuclear industry, the Small Ring Test (SRT), a miniature test derivated from the RHTT, has been investigated in recent years. In this investigation, a novel RHTT was designed to overcome the limitations of SRT and RHTT, and a new procedure was implemented to estimate the yield strength of tubes and pipes. Numerical FEM simulations were performed to reach an optimum estimation method for the yield strength with the specific geometry of the SRT and a wide selection of pipe geometries with the RHTT. A set of hypothetical materials were designed to perform these analyses, taking into account the influence of Young’s modulus, proportional limit, hardening coefficient (based on the Ramberg–Osgood law), and presence of Lüders bands straining. To verify the results obtained from this numerical FEM analysis, experimental tests (standard tensile tests and RHTTs) and metallographic analysis were performed on aluminum Al 6063 T6 and copper C12200 R360 tubes, showing the capability of this optimized RHTT to estimate the yield strength in the hoop direction for anisotropic tubes and pipes.