The process of production of complex coherent periodic structures on the sputtered material surface is investigated. The depth of the beam ion penetration to under the sputtered material surface depends on its form. This results in the sputtering coefficient local fluctuations corresponding to the surface roughness: the rate of cavity sputtering would exceed that one of hillocks. The related instability, developing under the surface sputtering can lead to the occurrence of surface structures. The basic unstable mode parameters (wave length, instability increment) are calculated within the framework of cascade theory and linear approximation. 8 refs.; 1 fig.