The first radial eigenmode of a nonaxisymmetric compressional wave in a cylindrical plasma surrounded by an insulating boundary is identified as a surface wave at low frequencies. The properties of these surface waves depend on the sign of the poloidal wavenumber m. For m positive there is a smooth change from surface wave behaviour at low frequencies to body wave behaviour at higher frequencies, typically around the ion cyclotron frequency. For m negative the wave has anomalous behaviour as it only exists below the ion cyclotron frequency and it resembles a torsional wave. The surface waves are first extensively analysed using a collisionless plasma model. Resistive effects are then included and are found to strongly modify the wave field profiles in a highly collisional plasma. Some comparison with experiment is given and further experiments are suggested.