Abstract Sine waves, circular arcs joined by straight lines, and meander-like waves have been reported to exist on flagella. These three waveforms are compared in terms of their analytical equations to find a means of distinguishing them experimentally. A Fourier analysis of the variation of tangent angle with arc length is suggested as the best method of discrimination. Expressions are derived for the hydrodynamic propulsive force and the elastic potential energy characteristic of each waveform. The waveforms are compared in the light of suggested mechanisms of flagellar activity.