The influence of size of particles on the X-ray fluorescence intensity for powdered substances with different sized particles is estimated, based on a simple modification of the Berry-Furuta-Rhodes formulae. Analytical expressions are obtained for the model of a powder substance consisting of particles of various sizes distributed randomly in the sample volume. The results of calculations by these expressions agree fairly well with experimental data for binary powder mixtures. The particle size effect on X-ray fluorescence for the powders presented is considerably more than one could be predicted by the models proposed earlier. (C) 2009 Elsevier B.V. All rights reserved.