To obtain the eigenmodes of the electromagnetic field at a periodically corrugated metamaterial we consider a theory of spoof plasmons propagating on metamaterial perforated with planar periodic grooves. We present the rigorous modeling and analysis of surface waves at the boundary of the corrugated metamaterial structure. Particularly, we pay special attention to the ways of controlling the properties of surface waves. Moreover, we analyze the dependence of the dispersion characteristics on the metamaterial design.