The mode matching method is applied to analyze generalized ridged waveguides. The tangential fields in each region are expressed in terms of the product of several matrices, i.e., a functional matrix about x-F(x), a functional matrix about y-G(y) and a column vector of amplitudes. The boundary conditions are transformed into a set of linear equations by taking the inner products of each element of G(y) with weight functions. Two types of ridged waveguide are calculated to validate the theory. Several new modes not reported in previous analysis are presented.