The interaction between particles and an advancing solid‐liquid interface has been investigated both experimentally and theoretically. For each particular type of particle, a ``critical velocity'' was observed, below which the particles are rejected by the interface, and above which they are trapped in the solid. The dependence of the critical velocity on various properties of matrix and particle was investigated. A theory has been developed, based on the assumption that a very short‐range repulsion exists between the particle and the solid. This repulsion occurs when the particle‐solid interfacial free energy is greater than the sum of the particle‐liquid and liquid‐solid interfacial free energies. The particle is pushed along ahead of the advancing interface and becomes incorporated into the solid if liquid cannot diffuse sufficiently rapidly to the growing solid behind the particle. Reasonable agreement was obtained between the calculated and experimentally observed critical velocities.