This report describes the MFIX (Multiphase Flow with Interphase eXchanges) compurer model. MFIX is a general-purpose hydrodynamic model that describes chemical reactions and heat transfer in dense or dilute fluid-solids flows, flows typically occurring in energy conversion and chemical processing reactors. MFIX calculations give detailed infor-" marion on pressure, temperature, composition, and velocity distributions in the reactors. With such information, the engineer can visualize the conditions in the reactor, conduct parametric • studies and what-if experiments, and, thereby, assist in the dessgn process. The MHX model, developed at the Morgantown Energy Technology Center (METC), has the following capabilities: mass and momentum balance equations for gas and multiple solids phases; a gas phase and two solids phase energy equations; an arbitrarynumber of species balance equations for each of the phases; granular stress equations based on kinetic theory and frictional flow theory; a user-defined chemistry subroutine; three-dimensional Cartesian or cylindrical coordinate systems; nonuniform mesh size; impermeable and semipermeable internal surfaces; user-_endly input data file; multiple, single-precision, binary, direct-access, output f'desthat minimize disk storage and accelerate data retrieval; and extensive error reporting. This report, which is Volume I of the code documentation, describes the hydrodynamic theory used in the model: the conservation equations, constitutive relations, and the initial and boundary conditions. The literatureon the hydrodynamic theory is briefly surveyed, and the bases for the different parts of the model are highlighted.