A compacting press having a support section, a compacting section which undergoes translational movement along a vertical axis (Z, Z') which is fitted with a thrust-plate and which forms a ram designed to compress cases by the application of pressure, and a guide assembly made up of a skirt, with a liner, a hoop and a cradle. The cradle is fitted to a skirt holding section by a removable connection made up of a reversible assembly system involving the fitting into place and horizontal movement of at least one key-hole shaped opening which passes vertically through the cradle and at least one vertically orientated mushroom-shaped lug. This press is preferably used for compacting a case containing hazardous materials, in particular radioactive waste.