An analysis is presented for the solution of the inverse radiation problem using a Monte Carlo technique. For inhomogeneous planar media, the profile of the single scattering albedo is obtained from the inverse analysis. For homogeneous, anisotropically scattering media, the single scattering albedo and the asymmetry factor are recovered. A step phase function approximation is used to account for the anisotropic scattering in the medium. The confidence bounds on the estimated parameters for errors in the input data are evaluated. The results show that the medium properties can be recovered with high accuracy even if there is up to 10% error in the input data. The primary advantage of the Monte Carlo method is that a single direct solution yields the coefficients of a multivariate polynomial for each set of observation data, which are then used to obtain the medium properties by a non-linear least-square minimization technique.