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The paper focuses on the calculation of mutual inductance between underground inducing line (underground power cable) and underground induced line (underground telecommunication cable). The calculation for the infinite integrals in the expression was simplified. The infinite integrals was converted to Watson infinite integrals by expanding the exponential function in series, so the known higher-order Neumann function and Struve function could be used to express the Watson infinite function, thus the numerical calculation problem for the mutual inductance between the underground power cable and the underground telecommunication cable is solved. The approximate expression which was more convenient to calculate could also be obtained, if the higher-order Neumann function, the first and the second item of expanded Struve function is fetched.