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An efficient method for calculating the reflection coefficient matrix of open-ended coaxial lines with an infinite flange is proposed in this letter. The matrix equation containing double surface integrals on the aperture can be derived using the mode-matching method. These surface integrals are then converted to line integrals in the spectral domain by the Sommerfeld identity. Then the matrix pencil method is employed to fit the integrands with exponential series so that the integrals can be analytically expressed in closed form. An open-ended coaxial line is considered to verify the validity of the formulation. It is shown that the proposed method is very efficient in calculating the reflection coefficient matrix of open-ended coaxial lines.