A four-dimensional (4D, in concentration–temperature coordinates) computer model of the isobaric phase diagram of uranium, sodium, magnesium, and plutonium chlorides, as well as four three-dimensional (3D) computer models of the phase diagrams of the ternary systems forming it, has been constructed. The technology of assembling a 4D model of 46 hypersurfaces and 17 phase regions was used in the design. The obtained 4D model of the UCl3–NaCl–MgCl2–PuCl3 phase diagram makes it possible to visualize a four-dimensional object as a whole (with all its hypersurfaces and phase regions) by any arbitrarily given 2D and 3D sections, as well as it is able to reproduce published (experimental or thermodynamically calculated) 2D sections. The scope of application of the results of the work is the development of materials for fuel components of fourth-generation molten salt reactors and pyrochemical recycling of spent fuel rods. For the first time, a comprehensive, complete description of phase diagrams composed of uranium, plutonium, sodium, and magnesium chlorides has been obtained.