A new approach, the multipole theory (MT) method, is described for the computation of axisymmetric modes (TE0 and TM0 modes) in rotationally symmetric cavities. The MT formulation of the eigenvalue problem related to the resonant frequencies is derived. Representative computational examples, including dual‐mode conductor‐loaded cavity filters and a cavity loaded with an inner conductor of complex shape, are given to validate the theory and to demonstrate the degree of its efficiency. © 2001 John Wiley & Sons, Inc. Microwave Opt Technol Lett 29: 412–415, 2001.