This report presents a method for predicting the r overage obtainable from a small ar/ay of waveguide apertures (20 -30 dB apert ire gain) over a large cylinder covered by dielectric (cylinder radius * 100 A).An infinite array model is developed, which shows that there are only minor differences between the pattern of an element in a dielec ric clad cylindrical array and that of an element in the corresponding planar c\rray. This result suggests that the coverage of a finite dimension array over a c/linder of large radius can be evaluated with good approximation by the means of a planar array model. The coverage of arrays in an infinite ground plane covered by dielectric is predicted hy developing a model which takes into account several waveguide modes in matching the fields at the array aperture interface. This model does not require the inversion of large matrices in determining the mutual coupling between array elements, thus permitting the analysis of relatively large arrays. This model shows that no coverage in the endfire direction is obtainable from these structures. To achieve endfire cove^gc the dielectric sheet covering the array must be of finite dimension.The coverage from a finite planar array covered by a finite dielectric, slab is predicted by assuming a simple but effective model of the radiation from the wedge terminating the dielectric sheet. This model shows that it i3 possible to obtain substantial coverage in the endfire direction by properly shaping the wedge at the expense of some pattern distortions. The overall array performance shows that it is possible to obtain hemispheric, scan coverage with maximum gain oscillation of no more than A. 5 dB. t»