Unlithified sediment at glacier beds should be entrained in ice as a result of melting above individual grains and refreezing below grains (regelation). To test this hypothesis, a device that simulates subglacial conditions was used to push ice downward through idealized and natural porous media in contact with a flat bed. Ice regelated toward the bed at speeds proportional to the gradient in ice pressure across the thickness of particles. Ice temperatures responded predictably to changes in driving stress and demonstrated that the ice-particle mixtures were at or very near the pressure-melting temperature. A theory of pore ice motion by regelation predicted the measured speed usually to within a factor of two, although at low driving stresses the speed was less than the predicted value by as much as a factor of five. The low speeds were probably caused by imperfect temperature control that resulted either in heat loss from the ice-particle mixtures or in slightly subfreezing pore ice temperatures that were not detected by thermistors. Ice should intrude the pores of underlying sediment to a steady depth at which the downward regelation speed equals the rate of basal melting. Departures from the steady state should cause release of debris from ice or further entrainment. An approximate calculation of the steady intrusion depth yields values comparable to typical thicknesses of debris in basal ice, a few centimeters to more than a meter. Intrusion of sediment by regelation is consistent with the isotopic composition of debris-bearing ice, if melting exceeds refreezing.