A method is proposed that drastically improves the computational efficiency of the spectral-domain method of moments applied to finite arrays of stacked microstrip antennas printed on electrically thick substrates. For that purpose a novel analytical method is proposed to calculate the integrals with infinite boundaries over the asymptotic part of the Green's function in closed form by using the theory of residues. For medium-sized arrays (50-100 elements), a total reduction of CPU time with a factor of 150 was obtained. Electrically thick substrates are taken into account by using a sophisticated model for the feeding coaxial cables that includes an attachment mode to ensure continuity of current at the probe-patch transition. Simulated and measured data of two medium-sized arrays are given. It is shown that the behaviour of edge elements significantly differs from the scan performance of the elements near the centre of the array.