In this paper, we present a numerical model for laser-plasma interaction involving Raman instability and Landau damping. This model exhibits three main difficulties. The first one is the coupling of PDE's posed both in Fourier space and in physical space. The second one is a three-waves resonance condition that has to be verified. The third one is the boundary conditions. We overcome these difficulties using, respectively a splitting scheme, a numerical dispersion relation and absorbing boundary conditions. We present some comparison between several phenomena that are involved and the influence of the Raman amplification and the Landau damping.