An analysis for the propagation characteristics of the magnetostatic surface waves in a YIG slab having periodically corrugated surfaces is presented. The Brillouin diagrams, close to the intersection point (&ohgr;,&bgr;) ofm=0 andm=−1 space harmonics, are obtained for different strengths of modulation. Comparison between the magnetostatic surface waves and volume waves concerning the complex value of the propagation constant within the stop band is also discussed.