A mathematical formalism is presented for calculating the mode spectrum and threshold condition for a corrugated distributed‐feedback laser. The procedure is applied to the case where the active medium is bounded by metallic walls. An expression for the coupling constant &kgr; which measures the amount of feedback per unit length is obtained. The complex transcendental equations relating the key parameters are shown to be of the same form as those deduced by Kogelnik and Shank for a periodic index variation.