A hybrid finite element method is presented for a characterization of scattering an radiation properties of microstrip patch and arrays residing in a cavity recessed in a ground plane. The technique combines the finite element and boundary integral methods to formulate a system for the solution of fields at the aperture and the scattering field and radar cross sections at free space. By virture of the finite element method, the proposed technique is applicable to patch antennas and arrays residing on or embeded in a layered dielectric loss/lossless substrate and is also capable of treating various feed configuration. Several numerical results are presented demonstrating the validity, efficiency and capability of the technique.