We study the properties of the intensity profiles scattered from the self-affine fractal random surfaces. Weuse the mathematical decay function to approximate the duple negative exponent function in the rigorous theory ofscattering, by letting them have the same maximum value and half-width, and the expression for the half-widths of theintensity profiles in the whole range of the perpendicular wave vector component is obtained. The previous results in thetwo extreme cases are included in the results of this paper. In the simulational verification, we propose a method for thegeneration of self-affine fractal random surfaces, using the square-root of Fourier transform of the correlation function ofthe surface height. The simulated results conform well with the theory.