Oscillatory density profiles (DP) are a well-known feature occurring at the free surfaces of liquid metals. We analyse first the layered structure of Hg at or below the melting temperature with a simple interaction model [J.-M. Bomont and J.-L. Bretonnet, J. Chem. Phys. 124, 054504 (2006)], by molecular dynamics simulation in slab geometry. Then, by investigating the in-plane structure, some state transitions are observed. In particular, crystalline planes, whose axes are tilted by several degrees from the surface normal, appear and seem to be signalized by flat DP.