A kinetic model of the formation of pyramid-like bulges (pedestals) at the bases of vertical nanowires is proposed. The formation of the pedestals at the early stage of the nanowire growth is assumed to be induced by a higher nucleation rate of two-dimensional islands under the catalyst droplet, as compared to the nucleation rate at the non-activated surface areas. Kinetics of the nucleation and propagation of the steps in the pyramid is described with a model of the multilayer growth, taking into account that the catalyst droplet at the nanowire top is a strong sink for adatoms. It is shown that the transition from the growth of the pyramid to the axial growth of the nanowire is possible if the appearance of a nucleus of the new layer under the catalyst droplet results in a partial dissolution of the underlying layer. In this case a segment of the nanowire sidewall is formed, preventing the lateral growth of the layers generated by the droplet.