A numerical method is presented for the problem of transverse magnetic or transverse electric scattering from infinitely long, lossy dielectric cylinders of arbitrary cross section. The method is based on the solution of a system of linear ordinary differential equations in the state-space form. The solution is achieved by finding the state transition-matrix and the zero-state response of the respective system. Numerical results are presented for cylinders of various cross sections, and they are compared with the results obtained by either exact or approximate numerical methods. ¿ 1999 American Geophysical Union