In the last ten years, observational evidences about a possible connection between Type Ia Supernovae (SNe) properties and the environment where they explode have been steadily growing. In this paper I discuss, from a theoretical point of view but with an observer's perspective, the usage of light echoes (LEs) to probe the CSM around SNe of Type Ia since, in principle, they give us a unique opportunity of getting a three-dimensional description of the SN environment. In turn, this can be used to check the often suggested association of some Ia's with dusty/star forming regions, which would point to a young population for the progenitors. After giving a brief introduction to the LE phenomenon in single scattering approximation, I derive analytical and numerical solutions for the optical light and colour curves for a few simple dust geometries. A fully 3D multiple scattering treatment has also been implemented in a Monte Carlo code, which I have used to investigate the effects of multiple scattering. In particular, I have explored in detail the LE colour dependency from time and dust distribution, since this is a promising tool to determine the dust density and derive the effective presence of multiple scattering from the observed properties. Finally, again by means of Monte Carlo simulations, I have studied the effects of multiple scattering on the LE linear polarization, analyzing the dependencies from the dust parameters and geometry. Both the analytical formalism and MC codes described in this paper can be used for any LE for which the light curve of the central source is known. ; Comment: 19 pages, 13 figures, accepted for publication in MNRAS. Full resolution version at http://www.eso.org/~fpatat/science/LE/paperI.pdf