An approximate approach is derived to enable a computer time-efficient prediction of multiple screen diffraction for grazing incidence. Comprehensive computations of multiple screen diffraction at up to ten randomly arranged screens were carried out using the Vogler method. On the basis of these numerical results, a suitable polynomial approximation is derived. In order to verify the approximation, the computations are repeated with different random screen distribution, and the deviation between the Vogler method and polynomial approximation is statistically evaluated.