Slurries of relatively fine particles of solids wastes and similar materials are disposed of through injection wells (24) which penetrate earth formation (13) disposal zones which have a minimum in situ compressive stress generally less than an overburden zone (14) and an underburden zone (18) adjacent to the disposal zone (16). The disposal zone preferably has a permeability greater than the overburden and underburden zones. The slurry is injected through a disposal well intersecting all of the zones and having perforations (44, 46, 48) preferably communicating the slurry with the underburden zone to provide for lateral growth of the hydraulically fractured disposal zone as the solids filter cake plates out on the fracture faces of the disposal zone without substantially penetrating the overburden zone.