Experiments are described in which the time-dependence of the sample thickness h(t) was measured for various soft solid materials squeezed between two parallel glass plates by a constant squeezing force F applied at t = 0. A yield stress for each material was also measured using rotational vane and serrated parallel-plate tools. Initially, the squeeze-rate V(t) = -dh/dt of all materials was fast and resembled that of a viscous fluid. Later, most materials showed a very small squeeze-rate, and h seemed to approach a finite plate-separation limit, characteristic of a yield-stress material. For some materials h appeared not to approach a finite limit, attributed to creep or thixotropy not evident in the more rapid vane and serrated parallel-plate measurements. Expressions which relate F to h(t) and V(t) for a Herschel-Bulkley material with stick or slip at the sample-plate interface were reviewed. No materials made frictionless contact with the sample-plate interfaces, and most were best-described by the Herschel-Bulkley squeeze-flow model of Sherwood and Durban (1998). The squeeze-flow data at very low shear rate did not support the existence of Newtonian high viscosity plateaux. A soft solid of closely-packed water-swollen particles swelled when F was decreased after a period of squeeze flow, suggesting relative motion between the constituent phases. The advantages and problems of using squeeze flow as a rheometrical technique are described and discussed.