IVA 2/001 is a computer code for simulating transient, three-dimensional, three-phase, three-component nonhomogeneous (three velocity fields), nonequilibrium flow in a cylindrical porous body (including nuclear reactor cores if desired). Each velocity field consists of an inert and a noninert component. A separated equation of field mass, inert mass concentration in each of the fields, and entropy of the fields together with mixture momentum equations for the flow are solved by a semi-implicit numerical method with an analytical reduction to the pressure or pressure velocity problem and backward substitution. The flexibility of the method in describing three velocity fields of arbitrary direction is demonstrated. The solution procedure of the hydrodynamic problem is described. Finally, a numerical example and a comparison with experimental data demonstrate that the IVA2 method is a powerful tool for numerical multiphase flow simulation.