Abstract: We studied structure and thermodynamic properties of cubic and tetragonal phases of pure uranium and U-Mo alloys using atomistic simulations: molecular dynamics and density functional theory. The main attention was paid to the metastable γ0-phase that is formed in U-Mo alloys at low temperature. Structure of γ0-phase is similar to body-centered tetragonal (bct) lattice with displacement of a central atom in the basic cell along [001] direction. Such displacements have opposite orientations for part of the neighbouring basic cells. In this case, such ordering of the displacements can be designated as antiferro-displacement. Formation of such complex structure may be interpreted through forming of short U-U bonds. At heating, the tetragonal structure transforms into cubic γs-phase, still showing ordering of central atom displacements. With rise in temperature, γs-phase transforms to γ-phase with a quasi body-centered cubic (q-bcc) lattice. The local positions of uranium atoms in γ-phase correspond to γs-phase, however, orientations of the central atom displacements become disordered. Transition from γ0 to γ can be considered as antiferro-to paraelastic transition of order-disorder type. \n\nThis approach to the structure description of uranium alloy allows to explain a number of unusual features found in the experiments: anisotropy of lattice at low temperature; remarkably high self-diffusion mobility in γ-phase; decreasing of electrical resistivity at heating for some alloys. In addition, important part of this work is the development of new interatomic potential for U-Mo system made with taking into account details of studied structures.