In this study, the freestanding form of ultra-thin CuI crystals, which have recently been synthe-
sized experimentally, and their strain-dependent properties are investigated by means of density
functional theory calculations. Structural optimizations show that single-layer CuI crystallizes in a
double-layered hexagonal crystal (DLHC) structure. While phonon calculations predict that single-
layer CuI crystals are dynamically stable, subsequent vibrational spectrum analyzes reveal that this
structure has four unique Raman-active modes, allowing it to be easily distinguished from similar
ultra-thin two-dimensional materials. Electronically, single-layer CuI is found to be a semiconductor
with a direct band gap of 3.24 eV which is larger than that of its wurtzite and zincblende phases.
Furthermore, it is found that in both armchair (AC) and zigzag (ZZ) orientations the elastic insta-
bilities occur over the strain strength of 19% indicating the soft nature of CuI layer. In addition, the
stress-strain curve along the armchair direction reveal that single-layer CuI undergoes a structural
phase transition between the 4% and 5% tensile uniaxial strains as indicated by a sudden drop of
the stress in the lattice. Moreover, the phonon band dispersions show that the phononic instability
occurs at much smaller strain along the ZZ direction than that of along the AC direction. Further-
more, the external strain direction can be deduced from the predicted Raman spectra through the
splitting rates of the doubly degenerate in-plane vibrations. The mobility of the hole carriers display
highly anisotropic characteristic as the applied strain reaches 5% along the AC direction. Due to
its anomalous strain-dependent electronic features and elastically soft nature, single-layer of CuI is
a potential candidate for future electro-mechanical applications.