Abstract : The evolution of random wave fields on the free surface is a complex process which is not completely understood nowadays. For the sake of simplicity in this study we will restrict our attention to the 2D physical problems only (i.e. 1D wave propagation). However, the full Euler equations are solved numerically in order to predict the wave field dynamics. We will consider the most studied deep water case along with several finite depths (from deep to shallow waters) to make a comparison. For each depth we will perform a series of Monte--Carlo runs of random initial conditions in order to deduce some statistical properties of an average sea state.