The branch of material science and nanotechnology has recently seen the emergence of a remarkable class of materials known as 2D materials. These materials have unusual features and behaviours because of their special two-dimensional structure that separates them apart from bulk materials. One of the characteristics of 2D materials are related to their capacity to handle large mechanical deformation without fracture. Since the discovery of graphene, researchers have discovered and created an extensive range of additional 2D materials with a variety of chemical compositions and topologies. These materials can be used for energy storage, sensing, catalysis and biomedical applications. In this thesis, electronic, vibrational, mechanic and chemical properties of singlelayer CuI were investigated by using density functional theory (DFT) based first-principles calculations. It is shown that the CuI structure crystallizes in a hexagonal lattice by energy and geometry optimizations. The vibrational properties of the material were examined by phonon and Raman calculations and the structure found to be dynamically stable and there were four Raman active modes. The electronic band dispersions and corresponding density of states showed that the single-layer CuI crystal has semiconductor nature with direct band gap. Strain calculations were performed to examine the mechanical strength of the CuI crystal. Effect of biaxial strain on the electronic band structure of CuI crystal was investigated in the range of ±5% and the direct band gap behaviour did not change. Biaxial and uniaxial strain calculations have shown that it is resistant to high stresses.