A fast analytical technique based on T-matrix approach is formulated to solve the problem of direct electromagnetic scattering by an infinite circular cylinder buried in a dielectric half-space and illuminated by a normally incident transverse magnetic (TM) plane wave. The technique employs the signal-flow graph (SFG) model to include all multiple reflections that take place during the scattering process. The selection of the truncation order of the obtained T-matrix is also discussed.