The authors consider the problem of two-dimensional scattering of electromagnetic waves by circular and elliptic cylinders and the calculation of the associated radar cross section. They allow for fields at infinity by introducing a fictitious absorbing layer at a finite distance from the cylinder. Various methods of calculation (finite-difference-time-domain, matched layer, perfectly matched layer) are compared and it is concluded that, in many cases, a perfectly matched layer method, using polar coordinates is the most satisfactory.