The intensity flux of the scattered radiation from x-ray beams in low atomic number materials has been obtained by a combination of analytical and Monte Carlo methods. Analytical methods were used to calculate the intensity flux of first-order scatter, and Monte Carlo methods to estimate the spectrum resulting from scatterings of higher order. The electronic computer at the University of Toronto was employed to obtain case histories for a pencil-like beam of photons with initial energies of 50, 100, 200, 500 and 1,250 kev impinging at right angles on a water scatterer. From the characteristics of the penetration of a pencil of rays, the properties of the diverging beams used in radiotherapy were obtained. Energy spectra were obtained for depths up to 20 cm. for areas of 25, 50, 100, and 400 sq. cm. and an infinite area. From these data for monoenergetic radiation, methods were developed to enable one to estimate the spectrum of scattered radiation produced by a continuous spectrum of incident radiations. By this means it is possible to estimate the spectral distribution of the scattered radiation for depths of 0, 2, 5, 10, and 15 cm. and areas of 25, 100, and 400 sq. cm. and infinite area for radiations in the range 50 to 1,250 kev. The energy absorbed, expressed as depth dose, was obtained for a number of incident spectra and compared with experimentally determined depth dose curves. The results were in good agreement.