A simulation method was developed for modelling SAXS data recorded on cellulose rich pulps. The modelling method is independent of the establishment of separate form factors and structure factors and was used to model SAXS data recorded on dense samples. An advantage of the modelling method is that it made it possible to connect experimental SAXS data to apparent average sizes of particles and cavities at different sample solid contents. Experimental SAXS data could be modelled as a superposition of a limited number of simulated intensity components and gave results in qualitative agreement with CP/MAS 13C-NMR data recorded on the same samples. For the water swollen samples, results obtained by the SAXS modelling method and results obtained from CP/MAS 13C-NMR measurements, agreed on the ranking of particle sizes in the different samples. The SAXS modelling method is dependent on simulations of autocorrelation functions and the time needed for simulations could be reduced by rescaling of simulated correlation functions due to their independence of the choice of step size in real space. In this way an autocorrelation function simulated for a specific sample could be used to generate SAXS intensity profiles corresponding to all length scales for that sample and used for efficient modelling of the experimental data recorded on that sample. Graphical abstract: [Figure not available: see fulltext.] © 2021, The Author(s).