The layered uranyl silicate clay-like mineral, uranophane-α, Ca(UO2)2(SiO3OH)2·5H2O, was studied by first-principles calculations based on the density functional theory method. The structure, observed in nature in a wide variety of compounds having the uranophane sheet anion topology, is confirmed here for the first time by means of rigorous theoretical solid-state calculations. The computed lattice parameters, bond lengths and bond angles were in very good agreement with the experimental ones, and the calculated X-ray powder trace accurately reproduced its experimental counterpart. The mechanical properties of uranophane-α, for which there are no experimental data for terms of comparison, were determined, and the satisfaction of the mechanical stability Born conditions of the structure was demonstrated by calculations of the elasticity tensor. The Raman spectrum was computed by the density functional perturbation theory and compared with the experimental spectrum. The vibrational properties of this mineral were well characterized, showing a good performance in all of the studied spectral range. Theoretical methods allowed assignment of the Raman bands to vibrations localized in different fragments within the crystal unit cell. Finally, the possibility of incorporation of strontium inside the uranophane structure was studied. The computed structure, X-ray powder trace and Raman spectrum of Sr-exchanged uranophane were very close to those of the ordinary Ca-uranophane.