Based on a new variational method, an even- and odd-mode analysis of transverse coupling slot between waveguides is presented. The proposed method is capable of dealing with slots of finite wall thickness. It uses multiple incident waves with symmetry to simplify the field distribution in the vicinity of the slot, enabling the adoption of one-expansion-term trial functions with sufficient accuracy, even in the instance of wide slots. Analytical solutions are provided, and the calculated results demonstrate excellent agreement with those of numerical simulation. The computation time with the new formulation is, however, significantly shorter.