A low dose technique has been recently proposed for tomographic studies of the lung, which makes use of a gamma camera to detect 90 degrees Compton-scattered photons from external planar gamma source. In this paper, we present a detailed Monte Carlo study of this technique. A 20 x 20 x 20 cm3 water phantom was simulated as a target and a large gamma camera equipped with an imaging collimator as a detector. The multiple scattering contamination of the single scattered signal was studied as a function of the source-detector geometry and of the incident energy in the range 100-500 keV. The multiple to single scatter ratio has an approximate 1/E0.7 dependence and increases almost linearly with the phantom depth and the transversal thickness at 90 degrees . Simulation has been also performed with a 16 x 16 x 10 cm3 sawdust phantom of 0.3 g/cm3 density; the Monte Carlo results agree to within a few percent with experimental data.