In the reconstruction of particle tracks in high-energy physics experiments multiple scattering has to be taken into account by computing the variance of the deflection and of the lateral displacement of the track both for discrete and for continuous scatterers. We apply this method to modelling the lateral position uncertainty in the target area in the context of ion therapy. The beam monitoring unit is treated as a discrete scatterer, tissue and bones of the patient as a continuous scatterer. By a simple model of the energy dependence of the scattering process the variance of the lateral displacement can be written down in closed form.By using just the variance of the lateral displacement it is not possible to describe the distribution in more detail, in particular the tails. If one wants to go beyond the Gaussian assumption, then it is convenient to model the distribution by a Gaussian mixture, in this case a mixture with only two components. One component describes the core of the distribution, the second one the tails. Starting from a thin scatterer, we compute the cumulants of the distribution in a scatterer of any thickness and show how to approximate it again by a Gaussian mixture with two components. We also show that under suitable assumptions the variance of the core reproduces very nicely the logarithmic correction formula which is usually applied to discard the tails in a Gaussian setting. In contrast, our approach yields a quantitative description of the tails which can then be used in the treatment planning for a fast and precise simulation of the effects of multiple scattering.