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The surface-wave diffraction at the edge of a finite-size substrate with a high dielectric constant is the dominant mechanism affecting the radiation pattern of a patch antenna fabricated on this material. A soft-and-hard surface (SHS) can be used to block the surface waves from propagating outward along the dielectric substrate, thus reducing the unwanted diffraction. Patch antennas surrounded by the SHS are analyzed using the finite-difference time-domain (FDTD) technique that implements the SHS boundary conditions using a simple modified subcell model. A square stacked-patch antenna and a circularly polarized (CP) patch antenna on a thick LTCC multilayer substrate are investigated. It is shown that the radiation pattern of the square patch on a big-size substrate can be significantly improved using SHS while the backward radiation level of the CP antenna with SHS on a small-size substrate is considerably reduced.