The volume averaged equations for convective melting of particles in a packed bed are developed and a simple model is proposed. The model is solved numerically in one dimension to predict melting rates for a single substance and a system in which the liquid phase at elevated temperature enters a packed bed of the solid phase at the melting temperature. Materials having the thermophysical properties of water and aluminum are examined. For large Peclet number, the heat transfer is dominated by convection and the melting rate depends on the Stefan number, liquid to solid density ratio, fluid velocity and the initial solid fraction. The thickness of the melting zone increases with Peclet number and Prandtl number for systems dominated by convection.