Summary: The orthogonal polynomial approach has been used to solve the guided wave propagation in structures for about 20 years, but was limited until now to one-dimensional structures, that is, structures with a finite dimension in only one direction, such as horizontally infinite flat plates and axially infinite hollow cylinders. This paper extends the orthogonal polynomial approach to two-dimensional structures, that is, structures with finite dimensions in two directions, with illustration on the multilayered rectangular rod. Through numerical comparison with the available results, the validity of the extended polynomial approach is illustrated. The dispersion curves and displacement distributions of various layered rectangular rods are obtained to show their guided wave characteristics.