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A hybrid method, which combines the UTD ray technique with the numerical MoM approach was introduced to provide a relatively efficient analysis of the EM radiation/scattering from an electrically large, planar, periodic, finite array (see Aydin Civi, O. et al., Radio Science, vol.35, no.2, p.607-20, 2000). That hybrid approach is extended to deal with arrays on grounded dielectric slabs. This work is of interest in the analysis of many practical arrays such as dielectric covered slot arrays, printed dipole and microstrip patch arrays, etc. It is well known that surface waves which are present in the grounded dielectric slabs can affect array mutual coupling, and can lead to effects of scan blindness in such arrays.