The finite element-boundary integral method is used in the context of stationary iteration techniques to solve for the radiation patterns of linear and planar finite arrays of identical elements. The radiating element is a cavity-backed slot/patch (CBS/P) antenna which is decomposed into an interior region and an aperture region. The array elements are coupled to each other through the aperture unknowns and the free-space Green's function. The resulting block matrix system is solved using one of three stationary block iterative techniques namely the Jacobi method, the Gauss-Seidel method and the successive over-relaxation method. An incomplete LU factorisation of the single-element matrix is used within the block iteration scheme. The rate of convergence and computational statistics of these block iterative techniques are examined and compared with each other. Conclusions are drawn on the effectiveness of each of these iterative techniques to tackle moderate to large finite arrays of CBS/P antennas.