We propose a simple analytical model for the elastic incoherent structure factor of proteins measured by neutron scattering, which allows extracting the distribution of atomic position fluctuations from a fit of the model to the experimental data. The method is validated by applying it to elastic incoherent structure factors of lysozyme which have been obtained by molecular dynamics simulation and by normal mode analysis, respectively, and for which distributions of the atomic position fluctuations can be generated numerically for direct comparison with the predictions of the model. The comparison shows a remarkable agreement, in particular, concerning the lower limit for the position fluctuations, which is pronounced in the numerical data.