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A computerized model of steady–state photon diffusion within turbid media such as biological tissues, solved by means of the Finite Element Method (FEM) is presented in this paper. Assuming that the different media are illuminated by a flat collimated laser beam source, we develop the basic theory including the suitable boundary conditions along the meshed domain. Model simulations depict firstly photon-flux density patterns in the $r-z$ plane associated with axis fluence rate profiles, plotted as functions of media properties and beam sizes. A second objective was to display both the rate of re-emitted optical power integrated by an optical fibre radially displaced away from the source and the power integrated by an optical fibre axially moved inside the tissue. Simulation studies are further extended to multilayered media such as skin and aorta, in order to describe the light propagation through these tissue structures more realistically.