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A method is given for the determination of the electromagnetic fields excited in accelerator cavities by a bunched beam of charged particles passing through the cavities. The electric and magnetic fields within a cavity are determined by solving a ``coupled regions'' problem, where the regions consist of a coaxial cavity and a cylindrical waveguide coupled through a gap. Numerical results are obtained by use of a digital computer for a few configurations representing linear accelerator cavities with drift tubes. The results are presented as a series of normalized curves of pertinent electrical quantities; they should give a clear qualitative picture of the effects of beam loading in linear accelerator cavities. Owing to space limitations, only the fundamental resonance excited by the fundamental beam harmonic was investigated in any detail. The general expressions advanced in this paper can be used to investigate higher‐order resonances excited by higher‐order beam harmonics.