It has previously been shown that there is close agreement between theoretical and experimental behaviour of pulses of ultrasound propagating in solid cylindrical waveguides. Waveguides are used in a number of areas of medical ultrasonics and it is therefore important to be able to model sound propagation in them accurately. This paper extends the analysis of guided wave propagation to hollow waveguides. In particular, frequency spectra of modes of progagation are given and theoretical group velocity curves are compared with experimental results. Signal strengths of modes propagating in both solid and hollow stainless steel waveguides of similar cross-sectional area are also compared.