A new approach, the multipole theory (MT) method, is presented for calculating two-dimensional (2-D) Helmholtz equation problems. By the mathematical deduction, the general MT formula and its applied laws are derived. The new approach has been applied to compute the cutoff wavenumbers of a rectangular waveguide, as analytical results are available for this problem. In order to further verify the accuracy of this method, the MT method has also been applied to compute the TE and TM modes of two high power waveguides and a square offset line. Comparison of accuracy is made whenever data is available. It has been proven that the MT method is an effective approach for calculating 2-D Helmholtz equation problems.