As an ice sheet slides over its sediment bed, some clasts partly embedded in the glacier sole plow through the bed surface. The size distribution of such clasts, if it can be characterized from structures in the geologic record, can be used to estimate the sliding velocity of a past ice sheet. By combining a theory of glacier sliding with a geotechnical theory of cone penetration, sliding velocity can be calculated in terms of clast-size parameters, a fluidity parameter for ice, and the thermodynamic properties of ice and clasts. If frictional properties of the bed are measured, the effective normal stress on the bed and bed shear strength during glaciation can also be calculated. We used this approach to estimate the sliding velocity of an Illinoian ice sheet that left plowing structures in cemented outwash near Peoria, Illinois. Fluidity parameters for normal and basal temperate ice yielded sliding velocities of 140--168 m yr-1 and 60--72 m yr-1, respectively. These are overestimates if solutes impeded regelation of ice past clasts or if friction between debris-laden ice and clasts retarded slip. Preconsolidation stresses determined in laboratory tests on silt from the bed agree with effective normal stresses calculated using clast-size parameters. The high shear strength of the bed (>145 kPa) and primary structures preserved within it indicate that additional movement due to pervasive shear of the bed was unlikely. Application of this method elsewhere would provide basal velocity data that are otherwise unavailable for testing and tuning of ice sheet models.