Experiments are described in which a constant force F squeezed a fluid, either between two parallel circular plates, or between a plate and convex spherical lens. Newtonian fluids obeyed the relation of Stefan (1874) for plates, and the relation of Adams et al. (1994) for plate and lens. The non-Newtonian yield stress fluids Brylcreem, Laponite and Sephadex were squeezed between plates of various diameter D to attain a stationary separation h. Only for separations greater than h* (which depended on the fluid) did Brylcreem and Laponite obey the relation F/D-3 proportional to h(-1) of Scott (1931) and give a yield stress in agreement with the vane method. For Sephadex the dependence of F/D-3 on h disagreed with Scott's relation, but varied as h(-5/2) for h > 0.6 mm and h(-3/2) for h < 0.6 mm. On rotating one plate in its plane the yield stress fluids at a fixed F suffered a marked decrease of h. This, and the existence of h*, are discussed in terms of the soft glassy material model of Sollich et al. (1997) and Sollich (1998). Brylcreem and Laponite were squeezed between a plate and lenses of various curvature and their yield stress obtained using the relation of Adams et al. (1994) was compared with measurements by plate-plate squeeze-flow and vane methods.