The bulk and surface electronic structure of α-SnS is investigated by X-ray photoelectron spectroscopy and band structure calculations, using ab-initio Hartree-Fock program CRYSTAL. Calculated band structure and density of states are consistent with recent calculations using other methods. Scanning tunnelling microscopy (STM) and Atomic Force microscopy (AFM) images were examined by calculating the partial electron density ρ(r, Ef) and total electron density ρ(r) of a slab which consists of height (100) α-SnS layers. It was found that bright spots in experimental STM images correspond to sulphur and tin atoms in positive bias voltage and to the outermost layer (tin atoms only) in negative bias voltage. However, the simulated image related to filled states cannot explain the new periodicity of the experimental pattern in low negative polarisation, which suggests the appearance of a surface charge density wave. The performed AFM image show a periodicity which can be simply explained by the atomic corrugation at the surface.