Abstract: According to the statistical model of the random phase screen, which is employed in the high power laser system, the phase noise and the first and second statistical characteristics of RMS gradient have been studied. The properties of the coherent and partially coherent lights after propagating through the random phase screen are discussed. Using the statistical model, the numerical simulation of the far-field distribution of the beams has worked out. The results show that the far-field distribution of the coherent light that propagates through the phase screen becomes unsymmetrical until the phase distribution satisfies the mathematical expectation. The partially coherent light will hold its Gussian-Schell-model charecter while propagating through the random screen. The character of the S