The research involving the crystal structures and properties of uranyl carbonate minerals is essential in actinide environmental chemistry due to the fundamental role played by these minerals in the migration of actinides from uranium deposits and nuclear waste repositories and in the investigation of accidental site contaminations. In this work, the crystal structure, hydrogen bonding network, X-ray diffraction pattern and mechanical properties of six important uranyl carbonate minerals, roubaultite (Cu₂[(UO₂)₃(CO₃)₂(OH)₂]·4H₂O), fontanite (Ca[(UO₂)₃(CO₃)₂(OH)₂]·6H₂O), sharpite (Ca[(UO₂)₃(CO₃)₄(OH)₂]·3H₂O), widenmannite (Pb₂[(UO₂)(CO₃)₂(OH)₂]), grimselite (K₃Na[(UO₂)(CO₃)₃]·H₂O) and čejkaite (Na₄[(UO₂)(CO₃)₃]), are investigated using first principles solid-state methods based in density functional theory. The determination of the positions of the hydrogen atoms in the unit cells of fontanite, sharpite and grimselite minerals, defining the hydrogen bonding network in their crystal structures, has not been feasible so far due to the low quality of their experimental X-ray diffraction patterns. The full crystal structures of these minerals are obtained here and their hydrogen bonding networks are studied in detail. Furthermore, the experimental structures of roubaultite, widenmannite and čejkaite, obtained by refinement from X-ray diffraction data, are confirmed. In the six cases, the computed unit-cell parameters and the associated geometrical variables are in excellent agreement with the available experimental information. Furthermore, the X-ray diffraction patterns computed from the optimized structures are in satisfactory agreement with their experimental counterparts. The knowledge of the full crystal structures, being extraordinarily relevant for many scientific fields, is also extremely interesting because it opens the possibility of determining their physico-chemical properties using the first principles methodology. The measurement of these properties under safe conditions is very expensive and complicated due to the radiotoxicity of these minerals. In this paper, a large set of relevant mechanical properties of these minerals are determined including their bulk, shear and Young moduli, the Poisson's ratio, ductility, hardness and anisotropy indices and bulk modulus pressure derivatives. These properties have not been measured so far and, therefore, are predicted here. Four of these minerals, roubaultite, fontanite, sharpite and widemmannite, are highly anisotropic and exhibit negative mechanical phenomena under the effect of small external pressures.