Absorbing material is used to reduce the Q factors of resonant cavities, enhance the bandwidth and restrain the competitive modes in high-power microwave devices. In this paper, solving field in absorbing material and field matching method were used to derive the dispersion equation in waveguides and field matching formulas of hybrid modes (HEM) in an abrupt cavity with absorber. Based on the theoretical analysis, numerical simulations of the cavities in gyroklystrons were done.The influence of absorber on transmission and attenuation in waveguides, the loss and resonance characteristic and quality factors in cavities has been studied. The main results are presented.