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For one-dimensional (1D) structures such as tubes, wires, and beams, tensile testing is a simple and reliable methodology for measuring their mechanical properties. The tensile offset angle effect on mechanical property measurement has long been ignored. In this study, theoretical and finite-element analysis(FEA) models for analyzing the tensile offset angle effect have been established. It is found that longitudinal stress decreases with increasing offset angles. The theoretically calculated elastic modulus relative errors reach 4.45% at the offset angle of 10°, whereas the experimentally measured elastic modulus relative errors are 45.4% at the offset angle of 15°. The difference in elastic modulus relative errors between the theoreticalanalysis and the experimental results is discussed with reference to the sensing system in the experimental instrumentation. To accurately measure the mechanical properties using the tensile testing technique, perfect alignment with a zero or small offset angle less than 5° is needed. A calibration methodology for aligning specimens has been developed.