The process uses a compression machine depositing the refuse, or the cover material onto the dump, with the refuse etc. discharged from the compression machine with a hopper onto the clump. The refuse etc. is transferred from a tilting container on the collecting vehicle into the machine hopper. Pref. the refuse etc. is compressed in the machine and forced onto the dump surface via a compression duct. The refuse is typically comminuted, crushed and compressed in the machine prior to forcing through the compression duct as a mash.