The estimation of particle fall velocities in viscoplastic materials is still full of uncertainties, despite the number of experimental studies and data correlations performed over the years by various authors. In addition to increasing the corpus of experimental data, the present paper develops a new method for direct (non-iterative) prediction of these velocities. Existing techniques employ the customary curve of drag coefficient versus Reynolds number, which has the major disadvantage that the required fall velocity occurs in both co-ordinates. A new curve (which can be applied to both Newtonian and non-Newtonian fluids) has been devised to overcome this difficulty, and thus eliminate the need for iteration. For non-Newtonian materials the new curve is used with an 'equivalent Newtonian viscosity', which has been calibrated against available experimental data. It is shown how this viscosity can be determined directly from the rheogram, without the need for a specific fit equation. (C) 2003 Elsevier Science B.V. All rights reserved.