Abstract: By means of density functional theory based first-principles calculations, the structural, vibrational, and electronic properties of 1H- and 1T-phases of single-layer CaX2 (X = F, Cl, Br, or I) structures are investigated. Our results reveal that both the 1H- and 1T-phases are dynamically stable in terms of their phonon band dispersions with the latter being the energetically favorable phase for all single-layers. In both phases of single-layer CaX2 structures, significant phonon softening occurs as the atomic radius increases. In addition, each structural phase exhibits distinctive Raman active modes that enable one to characterize either the phase or the structure via Raman spectroscopy. The electronic band dispersions of single-layer CaX2 structures reveal that all structures are indirect bandgap insulators with a decrease in bandgaps from fluorite to iodide crystals. Furthermore, the calculated linear elastic constants, in-plane stiffness, and Poisson ratio indicate the ultra-soft nature of CaX2 single-layers, which is quite important for their nanoelastic applications. Overall, our study reveals that with their dynamically stable 1T- and 1H-phases, single-layers of CaX2 crystals can be alternative ultra-thin insulators.