Newtonian fluids and non-Newtonian soft solids were squeezed between parallel glass plates by a constant force F applied at time t = 0. The plate separation h(t) and the squeeze-rate V(t) = -h were measured for plate roughnesses in the range 0.3-31 mum, and the results compared with predictions of theory. Newtonian liquids between smooth plates followed closely the prediction V alpha t(-3/2) after a short time, Many non-Newtonian materials showed a boundary-slip that was lessened or removed by plate roughnesses in the above range and for some the slip seemed to vary during the squeezing process. Perfect slip (zero boundary shear stress) was not approached by any material, even when squeezed by optically polished plates. For several soft solids the h(t) data resembled the predictions of squeeze-flow theory, and the yield stress obtained from the limiting value of h as V --> 0 was close to that measured by the vane method. However, the V(t) behaviour of most soft solids showed deviations from the prediction of theory, particularly for long squeezing times. For materials that had a continuous liquid phase in which other liquid or solid phases were suspended the deviations were consistent with phase concentration gradients induced by the squeezing process. (C) 2004 Elsevier B.V. All rights reserved.