This report describes the progress made on the design of the liquid hydrogen absorber for the international Muon Ionization Cooling Experiment (MICE). The absorber consists of a 21-liter vessel that contains liquid hydrogen (1.5 kg) or liquid helium (2.63 kg). The cryogen vessel is within the warm bore of the superconducting focusing magnet for MICE. The purpose of the magnet is to provide a low beam beta region within the absorber. For safety reasons, the vacuum vessel for the hydrogen absorber is separated from the vacuum vessel for the superconducting magnet and the vacuum that surrounds the RF cavities or the detector. The absorber has two 300 mm-diameter thin aluminum windows. The vacuum vessel around the absorber has a pair of thin aluminum windows that separate the absorber vacuum space from adjacent vacuum spaces. The absorber will be cooled using a heat exchanger that is built into the absorber walls. Liquid nitrogen is used to cool the absorber to 80 K. Liquid helium completes the absorber cool down and condenses hydrogen in the absorber. The absorber may also be filled with liquid helium to measure muon cooling in helium.