The MAX (Male Adult voXel) phantom has been developed from existing segmented images of a male adult body, in order to achieve a representation as close as possible to the anatomical properties of the reference adult male specified by the ICRP. The study describes the adjustments of the soft-tissue organ masses, a new dosimetric model for the skin, a new model for skeletal dosimetry and a computational exposure model based on coupling the MAX phantom with the EGS4 Monte Carlo code. Conversion coefficients between equivalent dose to the red bone marrow as well as effective MAX dose and air-kerma free in air for external photon irradiation from the front and from the back, respectively, are presented and compared with similar data from other human phantoms.