Nakajima et al, [Trans. Inst. Mining Metall. 87 (1978) C194] developed a method to measure the shape distribution of particles in terms of their size and thickness, This method was later extended to include models for square. rectangular, and circular aperture screens. In this project, the empirical equation for the probability of particles passing through the rectangular aperture screen in the Nakajima et al. model is replaced with a "basic probability" model and the results are compared. Next, regression equations relating the efficiency parameter of the model to selected screening operating variables are developed. Finally a "modified" Hatch and Mular model is introduced in the Nakajima et al. model and the results are compared with the experimental data. It is shown that both the new models fit the experimental results obtained from rectangular-aperture screens better than the original Nakajima et al. model. (C) 2002 Elsevier Science Ltd. All rights reserved.