Abstract: The problem of singular must be solved by method of moment for obtaining the cutoff wavenumbers of TM modein waveguides of arbitrary cross section . So they may be deficient in viz.speed and simplicity. This paper describes a convenientprocedure : at first the E-field integral equation has been obtained corresponding to the waveguide cutoff wavenumbers . Thenthe integral have been transformed into numerical method by Gauss-Legendre’s formula . The third the equation has beentransformed into a matrix equation using the method of moment . At last iterative technique has been used to pick out the eigenvalues of the matrix. it’s more laconicer because escaping singular