Slurried solid waste materials are injected into subterranean earth formations in a zone of interest (102) which has a relatively low in situ compressive stress (96) bounded by zones of higher in situ compressive stress (98, 100) and wherein the zone of interest has alternate layers of material of relatively high and low permeability to fluid flow, respectively. The solid waste slurry is conducted through an injection well (92) penetrating the zone of interest to form a conventional two-winged hydraulic fracture (132, 134). The fracture is extended by reducing the tendency to form filtercake in the fracture adjacent to the layers of material of relatively low permeability (142, 144) while depositing particle filtercake adjacent the earth layers of high permeability (146, 148, 150) so as to provide clear fluid flowpaths through the fracture while allowing the filtercake layers disposed in the fracture to assist in propping the fracture open.