Abstract Radial growth of vertically aligned nanowires involves formation and propagation of monoatomic steps at atomically smooth nanowire sidewalls. Here we study the step dynamics with a step flow model taking into account the presence of a strong sink for adatoms at top of the nanowire and adatom exchange between the nanowire sidewall and surrounding substrate surface. Analytical expressions for velocities of steps propagating from the nanowire base to the nanowire top are obtained. It is shown that the step approaching the nanowire top will slow down if the top nanowire facet is a stronger sink for adatoms than the sidewall step. This might trigger bunching of the steps at the sidewall resulting in development of the pencil-like shape of nanowires such as observed in, e.g., the Au-assisted MBE growth of InAs.