Abstract: Bi-directional analytical ray tracing (BART) was presented for calculating the scattering from conductive targets with electrically large size. In BART, the electromagnetic (EM) rays were assumed to be shot from both the sender and the receiver, and the bouncing on the conductive faces was traced. To speed up the tracing progress, the EM ray beams were expressed as analytical triangles, which could be calculated by triangle operations. In this paper, the extended BART (E-BART) is extended to calculate the radar cross section(RCS) of the lossy dielectric objects with electrically large size. In E-BART, both the reflected and the refracted rays should be taken into consideration on the lossy dielectric surfaces. The complex Snell-Descartes and Fresnel laws of lossy dielectric media indicate that the direction of wave propagation is determined by the equal-phase plane and the attenuation is calculated along the direction of equal-amplitude plane. In addition, the PO/GO transformation matrix is derived to modify the Green function from dielectric media to free space. Compared with the FEKO software, E-BART is proved to be accurate and effective.