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The perfectly matched layer (PML) is very popular and efficient for grid truncation of open-region problems. The concept of PML was introduced by J. P. Berenger (see J. Comput. Phys., vol.114, p.185-200, 1994) together with a numerical implementation based on the finite-difference time-domain (FDTD) scheme. However, the basic FDTD scheme is formulated on Cartesian grids and in many cases an unnecessarily large free-space region must be discretized between the PML and the object under investigation. F.L. Teixeira et al. (see IEEE Trans. Antennas Propag., vol.49, p.902-7, 2001) developed a conformal PML for the FDTD scheme. We continue this effort by presenting a new conformal PML formulation for the finite element method (FEM) in the time domain. It is based on the anisotropic material which has been used for the time domain FEM by D. Jiao et al. (see IEEE Antennas and Propag. Soc. Int. Symp., vol.2, p.158-61, 2002). We present the 2D-version of the conformal PML, which is a special case of our 3D-formulation. Furthermore, we consider only radar cross section (RCS) computations based on the scattered field formulation and emphasize that our PML is applicable to the total field formulation as well as radiating structures.