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Abstract—The oil and gas industry requires standardized testing of tubular products. Testing to the edges of a specified test envelope or yield criterion is performed in order to qualify designs. The most commonly used yield criterion for ductile steel tubular products is the von Mises-Hencky theory which provides a yield criterion based on a triaxial stress state. The yield criterion is used with real time data to model and predict possible impending yield of a test sample and provide notification to a test operator. For a significant portion of the standardized testing, the form of the yield criterion is an ellipse based on a triaxial stress state created by axial, hoop and radial stresses. The criterion is converted to axial loads and pressures and divided into two independent biaxial stress states that are recombined to provide the resultant yield surface or test envelope. The yield equations can be transformed such that a radial stepping technique can be used to produce a calculated yield surface that has the requisite resolution to define the areas of rapid curvature change. The algorithm presented provides sufficient resolution for real time comparison of loads to the yield surface or test envelope to predict possible yielding before potentially damaging expensive test samples.