Self-shaping and propagation of intense laser beams of different radial profiles in plasmas is investigated. It is shown that when a relativistic elliptically Gaussian beam propagates through an underdense plasma, its radial profile will self-organize into a circularly symmetric self-similar smooth configuration. Such self-similar propagation can be attributed to a soliton-like structure of the laser pulse. The anisotropic electron distribution results in a circular electric field that redistributes the electrons and modulates the laser pulse to a circular radial shape.
