This paper proposes a method for obtaining stresses in a rod with arbitrary cross section. The rod consists of two infinite straight portions and one two-dimensional curved portion in which the cross section varies. A twisting wave propagates from one of the two infinite straight portions to the other via the curved portion. In this analysis, fundamental equations were extended in order to apply them to the non-circular cross section by using the Fourier expansion collocation procedure, and the transfer matrix was derived. At connecting sections, solutions of curved portion and those of straight portions have been connected. Then it is possible to obtain the principal stress and the principal shearing stress at any location.