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A novel analysis for computing the admittance characteristics of edge slots with a salient feature in successfully considering the finite waveguide wall thickness is presented. The variational equation for the electric field in the slot region between the inner and outer waveguide walls is derived by applying the variational reaction theory and solved by the finite-element method. The division of the slot region into small elements of triangular cylinders and the basis function for each element are described in detail. In the limiting case of zero wall thickness, this finite-element analysis is reduced to a moment-method analysis using Galerkin's approach with triangular basis functions. The effects of waveguide wall thickness on the characteristics of the slot are investigated by comparing the numerical results with and without considering the wall thickness. Negligence of the wall thickness may result in a severe underestimation of the resonant length by as large as 14% for edge slots cut in typical X-band waveguides. The computed results with the finite wall thickness taken into account have been checked with the measured data published in previous literature and those obtained by a carefully devised experimental setup. Good agreement between theoretical and experimental results is obtained to demonstrate the validity of the analysis.