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A one-dimensionally rough random surface with known statistical properties was generated by digital computer. This surface was divided into many segments of equal length. The moments method was applied to each surface segment assuming perfect conductivity to compute the induced surface current and subsequently the backscattered field due to an impinging plane wave. The return power was then calculated and averaged over different segments. Unlike numerical computations of scattering from deterministic surfaces, problems of stability (as defined by Blackman and Turkey ) and convergence of the solution exist for random surface scattering. It is shown that the stability of the numerically computed estimate of the backscattered average power depends on , the total number of disjoint surface segments averaged; , the spacing between surface current points; , the width of each surface segment; and , the width of the window function. Relations are obtained which help to make an appropriate choice of these parameters. In general, choices of , and are quite sensitive to the incident wavelength and the angular scattering properties of the surface.