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In this paper, Robinson's analytical formulation is extended to calculate the shielding effectiveness of an shielding enclosure at off-axis observation points with an off-axis aperture. First, we give the procedure of extending the original analytical formulation. Then, the transmission-line matrix method (TLM) is utilized to validate the extended analytical formulation. The application range of the extended method is decided by comparing to TLM, and the good agreement between the results calculated by two methods indicates that the extended analytical formulation is efficient in predicting the shielding effectiveness of an enclosure at different observation points with an off-axis aperture. Through the intensive calculation and analysis, the distribution of SE inside the enclosure and the variation of SE with aperture position can be obtained, which may be used as a guideline for designing shielding enclosures.