This paper presents a circuit model of the thermoviscous acoustic wave propagation in waveguides with annular cross section. The model, validated against finite element method simulations of the input acoustic impedance, captures the annular waveguide behavior with good accuracy within a frequency bandwidth consistent with the lumped-element approximation. The cascading of multiple circuit models easily allows extending the bandwidth while preserving the same accuracy. The circuit model was derived from the low reduced frequency (LRF) wave propagation model in rectangular layers, representing a valid approximation of the complex LRF solution in annular waveguides. The simplified analytical description allows for the formulation of a compact T-network model comprised of standard circuit elements. This circuit model can be implemented in circuit simulators to accelerate both the analysis and engineering of devices having elements with annular cross section, such as micro-electro-mechanical systems devices or microphones.