Foam sheets are continuously produced by metering foam particles, which are free of any added binder or adhesive, from a storage location onto a moving conveyor at a controlled volumetric rate so as to continuously form a layer of the particles on the conveyor, heating the layer of particles to a temperature sufficient to render the particles tacky such that the particles adhere to one another so as to form a substantially integral sheet, compressing the sheet with a compression device that applies pressure on the advancing sheet so as to compress the sheet to a smaller thickness and enhance the integrity of the sheet; and cooling the compressed sheet.