In this article, we propose a new mathematical approach for the computation of electromagnetic wave amplitudes in grazing incidence X-ray fluorescence (GIXRF)-an analytical method for surface and near-surface layer analysis. The new contribution comes from an applied point of view, in order to have stable and fast algorithms to simulate the fluorescence intensity from a stacking of thin layer films. The calculation of transmitted/reflected amplitudes is an important part of the direct and/or inverse problem. An analysis of the amplitude versus layer thickness is also given. (C) 2015 Elsevier B.V. All rights reserved.194 3342