The energy of the field due to two charges as described by the field equations of the unquantized Born-Infeld theory is calculated to the first approximation in the case of stationary charges not subject to other external fields. The method of representing the field as the superposition of plane waves in a very large cavity is applied to the field equations expanded in a power series in the constant $\frac{1}{b^2}$ of the Born theory. For the first term this leads to the usual Coulomb energy. The process is then extended to calculate the second term from insertion of the coefficients arising in the first term evaluation. In this case it is found necessary to perform threefold averages in place of the previous single averages, since three of the radiation oscillators describing the field enter into combination. The resulting energy is $\frac{e_1{e}_2}{r[1-\frac{\left(\frac{1}{b^2}\right)({e_1}^2+{e_2}^2)}{8r^4}]}$. The nature of the series expansion makes the method invalid in the region near ${10}^{-13\mathrm{}}$ cm since there the series becomes divergent.

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