A solution is presented for the calculation of mutual coupling between elements in a finite planar rectangular waveguide antenna array. The aperture dimensions can be less than the feeding, waveguide dimensions and the elements are uniformly spaced in each of two directions in either a rectangular or isosceles triangular lattice. The problem is formulated as an integral equation by requiring the transverse electric and magnetic fields to be continuous across the apertures. The integral equation is solved by the method of moments for the equivalent magnetic current in the aperture region. A single expansion function is used to approximate the electric field in each aperture. For apertures that are close together the normal quadruple half-space admittance integral is reduced to single integrals which are evaluated numerically. For apertures father apart, a double numerical integral solution is used. In addition, the symmetry property of the symmetric Toeplitz admittance matrix for the linear array case and the symmetric block-Toeplitz admittance matrix for the rectangular array case is utilized when solving for the unknown magnetic current coefficients.