Particle‐in‐cell simulation has been performed to study the spatial‐temporal evolution of the pulse propagating in an underdense plasma. The spectra both of the reflected and transmitted radiation are investigated. The spectrum structure of the reflected radiation is due to the backward stimulated Raman scattering meanwhile the transmitted radiation structure is mainly due to the nonlinear self‐phase‐modulation. The influence of the pulse shape on the transmitted radiation spectrum is revealed. The dependence of the main features of the spectrum and the self‐consistent pulse distortion is found. The pulse distortion is accompanied by the relativistic electrons generation.