Summary: Three-dimensional travelling wave solutions are found for pressure-driven fluid flow through a circular pipe. They consist of three well-defined flow features – streamwise rolls and streaks which dominate and streamwise-dependent wavy structures. The travelling waves can be classified by the \(m\)-fold rotational symmetry they possess about the pipe axis with \(m = 1,2,3,4,5\) and \(6\) solutions identified. All are born out of saddle-node bifurcations with the lowest corresponding to \(m = 3\) and traceable down to a Reynolds number (based on the mean velocity) of 1251. The new solutions are found using a constructive continuation procedure based upon key physical mechanisms thought generic to wall-bounded shear flows. It is believed that the appearance of these new alternative solutions to the governing equations as the Reynolds number is increased is a necessary precursor to the turbulent transition observed in experiments.