A field theory for the magnetostatic surface wave (MSSW) reflectivity of a single shallow groove etched on top of an epitaxial YIG film is presented. Computed reflection characteristics are obtained for the case in which the grooved YIG film is unmetallized, and compared to corrected results for a metallized geometry. The conditions under which the MSSW reflctivity of a groove is significantly larger than the SAW reflectivity of an equivalent groove on a LiNbO3substrate are pointed out.